Nonhelical state

On the other hand, the equilibrium constant K indicates the tendency to form helical or nonhelical states. K values in excess of unity denote helix formers K values much less than unity, conversely, indicate coil-forming sequences. With proteins, proline, serine, glycine, and aspartine, for example, are typical helix breakers. Lysine, thyrosine, aspartic acid, threonine, arginine, cysteine, and phenyl alanine act as neither helical breakers or formers, whereas all other a-amino acids are typical helix formers. 

Rgureie Diagram of states of the C3 discotic of Figure 13 in the solvent n-butanol. The symbols represent data obtained by various experimental methods, and the lines the theoretical fits to the experimental data [75]. At low concentrations of material the monomers polymerize directly into helical polymers, while at higher concentrations a nonhelical polymerized regime intervenes. The demarcation of the monomeric and the polymeric regimes is set at 50% fraction material in polymers, rt= and that between the helical and nonhelical states by a 50% fraction of helical bonds, 0 =. ... 

The chiral catalyst 142 achieves selectivities through a double effect of intramolecular hydrogen binding interaction and attractive tt-tt donor-acceptor interactions in the transition state by a hydroxy aromatic group [88]. The exceptional results of some Diels-Alder reactions of cyclopentadiene with substituted acroleins catalyzed by (R)-142 are reported in Table 4.21. High enantio- and exo selectivity were always obtained. The coordination of a proton to the 2-hydroxyphenyl group with an oxygen of the adjacent B-0 bond in the nonhelical transition state should play an important role both in the exo-endo approach and in the si-re face differentiation of dienophile. 

In a very broad overview of the structural categories one can state several statistical correlations with type of function. Hemes are almost always bound by helices, but never in parallel a//3 structures. Relatively complex enzymatic functions, especially those involving allosteric control, are occasionally antiparallel /3 but most often parallel a//3. Binding and receptor proteins are most often antiparallel /3, while the proteins that bind in those receptor sites (i.e., hormones, toxins, and enzyme inhibitors) are most apt to be small disulfide-rich structures. However, there are exceptions to all of the above generalizations (such as cytochrome cs as a nonhelical heme protein or citrate synthase as a helical enzyme), and when one focuses on the really significant level of detail within the active site then the correlation with overall tertiary structure disappears altogether. For almost all of the dozen identifiable groups of functionally similar proteins that are represented by at least two known protein structures, there are at least... 

If the first bond can for whatever reason only be of the nonhelical (disordered) kind, then a helical polymer has to be nucleated if this nonhelical bond represents an excited state, so g > 0. The size of the critical nucleus depends in that case on how favorable the helical bond is relative to the nonhelical bond, in other words, on how strongly negative h is, and on the frustration free energy / > 0 because there is at least one monomer involved in two types of bonding. Within the model, the assemblies of size 2 < N <2-(j + g)/(g + h) with h < — g < 0 are high-energy structures and are therefore statistically suppressed. 

According to these considerations, a is a measure of the effects produced by the helix sequence ends. Of course, the monomeric units situated at these ends experience a different environment because of the nearness of the nonhelical sequences as they would in the center of the helix. It has been found that a is very small for proteins and poly(a-amino acids) (Table 4-12). So, end effects are not favored by these polymers. Thus, if a helical state of four monomeric units is separated from another helical state of three monomeric units, a helical state of seven monomeric units will tend to form. 

Rgure12 Schematic of helical supramolecular polymerization. Monomeric, nonhelical polymeric and helical polymeric states are in thermal equilibrium as indicated by the arrows. The equilibrium constants between the various species may differ greatly in magnitude. If helical polymers cannot form directly from the monomers, they need to be nucleated through the formation of nonhelical chains that may be energetically unfavorable. 

The crossover from the nonhelical to the helical polymeric state occurs for 5 = 1, and becomes sharper the smaller the value of the parameter a. It is for this reason that a is often viewed as a parameter that describes the cooperativity of the helical transition [72], This quantity is accessible experimentally by means of circular dichroism ectroscopy because to leading order in the temperature we have In 5 = A/ihCT - Th)/k 1 and (d9/dT)T=Ti, = A/th/4Va B T. Here, Th denotes the helical transition temperature where 9 = j, and Ahh the excess enthalpy associated with the formation of a helical bond [3]. The steepness of the measured helicity versus temperature curve (obtained, for example, by means of circular dichroism spectroscopy) depends on the ratio Ahbl /o, where Ahb is obtainable independently from microcalorimetry [71], Values of = 0.01 - 0.001 and Ahb 50 kJmoP have been obtained for the discotic of Figure 13, suggesting that the helical transition in supramolecular polymers can indeed be highly cooperative [3,73]. 

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