Learning from Synthetic and Biological Polymers
Many biological polymers undergo conformational changes between ordered and disordered states in a highly cooperative manner . Examples include the helix-coil transition in peptides  and nucleic acids , the beta-sheet to coil transition in peptides [55, 56], and the denaturation of proteins  and RNA . Co-operativity can provide a powerful way for supramolecular organization and it is a design principle ideally suited to chain molecules such as foldamers.
Cooperative transitions are characterized by abrupt changes as denaturing conditions such as high temperatures or unfavorable solvents are introduced. The signature of cooperative behavior is a sigmoidal shape in plots of spectroscopic or other conformationally dependent properties as a function of temperature or solvent composition. In contrast, a non-cooperative process only shows gradual changes. Figure 3.1 shows the characteristic behavior of two-state (first order) and one-state (higher order) cooperative transitions. A plot of free energy vs. conformation for a polymer that undergoes a two-state transition shows double minima, separated by a barrier. For such a transition both states are equally populated at the midpoint of the transition. In contrast, a single, broad population distribution and a single minimum in the free energy plot are indicative of one-state behavior. It can be seen from Fig. 3.1 that both types of behavior are capable of producing sigmoidal curves. Thus, it is not possible to distinguish between a one-state or a two-state transition simply on the basis of the appearance of a sig-
moidal curve. Rather, this distinction must be determined by an analysis of how the population of conformers changes throughout the course of the transition.
Solvents play critical roles in the cooperative behavior of biomolecules. In spite of the fact that the a-helix is the most abundant element of secondary structures in native proteins, many helix-forming sequences are only marginally stable in water [58, 59]. However, solvents such as 2,2,2-trifluoroethanol (TFE) are known to stabilize the a-helical conformation of short peptides [60, 61]. Peptide sequences were reported to undergo cooperative transitions to their a-helical state when TFE was titrated into an aqueous solution . In these cases, helix stability has been shown to follow a linear free energy dependence on TFE composition, analogous to the relationship that is often used to describe the denaturation of proteins by reagents such as urea or guanidinium salts .
A change in solvent composition often causes huge conformational changes in synthetic polymers. As the quality of the solvent decreases, flexible homopolymers tend to collapse into globular conformations . Formation of these collapsed conformations is intimately related to the (poor) solvation of the polymer chains. This coil-globule transition is known to be cooperative and is generally described as a second-order process, although simulations have shown that firstorder (two-state) transitions are possible for stiff chains  and polymers whose segments have long-range attractive potentials . Calorimetric studies on poly(N-isopropylacrylamide) indicate that the coil-globule transition for low molecular weight polymers follows a two-state process [66, 67]. Conformational transitions of this type have thus often been compared to the denaturation of small proteins, a process that also tends to follow a cooperative, two-state transition model between the native and the denatured state [68, 69]. Unlike proteins, however, homopolymers do not generally collapse to a unique conformational state . In fact, it has been shown that the size of the ensemble of compact conformations grows exponentially with chain length [71, 72].
Are there any advantages in using solvophobic and van der Waals interactions to create foldamers with biomolecule-like, cooperative conformational transitions?
An obvious one is related to their strength in aqueous solutions. In fact, water represents the ideal environment for these interactions due to its small size, high cohesive energy, and low polarizability [2-8]. Nevertheless, it seems much better to use strong, selective, and highly directional forces such as hydrogen bonds if one wants to obtain foldamers with highly organized conformations, despite their instability in water.
Lack of directionality in solvophobic and van der Waals interactions may be a huge disadvantage in using them for foldamers if one does not know how to take advantage of this feature. Nondirectionality itself, however, is not a deficiency and can be quite important to the conformational change. A large number of intramolecular interactions need to work together to allow a chain to undergo a cooperative transition to a non-degenerate conformation. Cooperativity asks that these interactions be weak individually but strongly coupled to one another through the conformation and covalent geometry of the foldamer chain. Solvophobic and van der Waals interactions are ideal in this regard, for both are "collective" interactions among a large number of solvents or polarizable bonds. In fact, one of the most accepted models for cooperativity in proteins is hydrophobic clustering, which states that hydrophobic collapse, at least in the early stages of folding kinetics, is directly responsible for cooperativity .
Because cooperativity demands multiple points of contact, it is easy to imagine highly directionally restricted forces would have little margin for error, whereas weak, non-directional forces tend to be more forgiving. One potential difficulty with highly directional forces (especially strong ones) is that a secondary structural design might quickly become over determined and incapable of yielding the desired conformation. If the ideal geometry of a directional interaction cannot be maintained within a covalently linked backbone, the mismatch would propagate as the chain lengthens. Another issue, probably a most serious one, is related to how well a successfully designed foldamer may serve as a platform to be modified and endowed with functional groups. It is easy to see that conformational motifs are more likely to be retained in foldamers based on ''fuzzy'' interactions such as solvophobic and van der Waals than those based on highly directional forces when different, functional monomers are inserted into the original sequence.
To successfully employ nondirectional interactions in a foldamer, one cannot use backbones with too many degrees of conformational freedom. Flexible homopolymers have rough energy landscapes and highly degenerate native states. Such chains are likely to collapse to a poorly defined compact globule. It seems that a key element for designing a foldamer organized by van der Waals and solvopho-bic interactions is the molecular contact area per degree of conformational freedom. Maximizing this ratio should help ensure stability of the folded structure as well as reduce degeneracy of the native state. Such a strategy indeed is widely used by nature to simplify the problem of conformational control. For example, amide bonds, which make up one third of the backbone of a natural protein, are rotationally restricted due to conjugation. Polysaccharides are also rigidified by their cyclic monosaccharide units. In the case of solvophobically based foldamers, rigidity has one additional benefit. When flexible molecules go from the solid phase to a solution phase, flexibility favors the latter by a favorable entropic contribution. Rigid molecules, on the other hand, do not benefit as much in such a transition. Essentially, solvophobicity can be enhanced by the rigidity of a molecule. (Low solubility of rigid molecules is also a result of high crystallinity and/ or strong intermolecular forces.)
Another important feature of proteins is amphiphilicity. In order for a solvophobic molecule to be soluble at all, it must be equipped with solvophilic segments. Amphiphilicity, however, is far more important than just providing solubility to biopolymers. Folding of proteins has been studied with the lattice model [70, 73]. In the simplest model, a peptide chain consists only of two types of units, labeled either as hydrophobic (H) or polar (P). These models showed that hydrophobicity was highly restrictive, quite counterintuitively for a nondirectional force. If a ''native'' conformation is defined as one with maximum number ofhy-drophobic interactions, sequences that can configure only into one or a few native conformations far exceed those that can assume 10 or more native conformations . Although not sufficient to give a single native structure to the peptide chain of a protein, hydrophobicity can constrain the chain into a relatively small number of compact conformations . This distribution of solvophobic and solvophilic segments is part of the connotation we intend for geometrical manipulation. In the meso- and macroscale self-assembly, shape, size, and pattern of solvophobic patches are sufficient to yield prescribed final structures . Doing so on the molecular scale is much more challenging, but is a skill chemists have to master in order to approach nature's ability in designing complex structures, especially when secondary folding motifs are integrated to form tertiary and further to quaternary structures.
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