Thermodynamics

When confining a foldamer strand to a specific conformation, in general the enthalpy gain due to attractive noncovalent interactions has to compensate for the entropy loss associated with the molecules' reduced conformational freedom. In solution, the most important contributions arise from the gain in enthalpy of the intramolecular contacts (DHF) and the loss of conformational entropy (DSconf(Fj) as shown in eq. 1:

We anticipate that the situation at the interface is seemingly more complex involving several enthalpic and entropie terms (eqs. 2 and 3):

Important additional enthalpic components (eq. 2) are associated with intermolecular association ([email protected]), interfacial foldamer-surface interactions ([email protected]) as well as desolvation of both the foldamer molecule (AHdesolv(F)) and the interface (AHdesolv(I)). Furthermore, additional entropic factors (eq. 3) include the transla-

AH = AHf + [email protected] + [email protected] + AHdesolv(F) + AHdesolv(I)

AS = ASconf (F) + AStrans(F) + ASrot(F) + ASdesolv(F) + ASdesolv(I)

tional and rotational entropy of the foldamer chain (AStrans(F) and ASrot(F)} as well as the entropy associated with desolvation of the foldamer (ASdesolv(F)} and the interface (ASdesolv(i)}, respectively. To simplify the thermodynamic treatment, we assume the interfacial foldamer-surface interactions ([email protected]) to be the dominating additional factor. The consequence is illustrated with the aid of a simplified model [3], comparing the folding of a homosequence foldamer with isoenergetic interactions between repeat units into either helix or sheet conformation in solution and at the interface (Fig. 13.3).

Fig. 13.3 Thermodynamics of folding into helix vs. sheet conformations in solution and at interfaces. Dominant intramolecular (black dotted) and interfacial (red solid) enthalpic interactions give rise to different thermodynamic behavior (bottom), where the most important energetic contributions (bottom) arise from enthalpy gain due to intramolecular (AHf shown in black) and intermolecular ([email protected] shown in red) interactions and entropy loss due to conformational confinement (ASconf(F) shown in blue).

Fig. 13.3 Thermodynamics of folding into helix vs. sheet conformations in solution and at interfaces. Dominant intramolecular (black dotted) and interfacial (red solid) enthalpic interactions give rise to different thermodynamic behavior (bottom), where the most important energetic contributions (bottom) arise from enthalpy gain due to intramolecular (AHf shown in black) and intermolecular ([email protected] shown in red) interactions and entropy loss due to conformational confinement (ASconf(F) shown in blue).

In solution, folding into the helix conformation is associated with a nucleation event, which leads to preorganization of the first attractive intrastrand interaction between non-neighboring repeat units and therefore helix folding is cooperative. Folding into a sheet at the single molecule level is however not cooperative since the intrastrand interactions involve neighboring repeat units. It is important to realize that the folding into individual sheets is barely observed due to concurrent aggregation that is mediated by attractive interchain contacts and proceeds in a cooperative fashion due to preorganization.

It is expected that at the interface, the interfacial interactions dominate and as a consequence both helix and sheet conformation are stabilized, however, to a different degree. In our simplified model (Fig. 13.3), the helix can only use every third repeat unit to engage in attractive molecule-surface interactions, while the sheet is able to utilize every single residue. While this particular model is certainly largely simplistic, it illustrates some important differences when comparing folding at the interface to folding in solution, most importantly:

1. The nucleation barrier is lowered.

2. The critical chain length is decreased.

3. A smaller number of helix repeat units is favored.

4. Usually sheet formation is more favored due to the adsorption geometry since usually fewer residues can interact with the surface in the case of the helix as compared to the sheet, i.e. flat vs. curved adsorbate.

Another important aspect is related to the reversibility of the molecule-surface interactions, which is a necessary prerequisite for equilibration and hence defect healing and fidelity of pattern recognition. The ''entropic distraction'' involved in the recognition of a patterned surface by an oligomer/polymer strand displaying interacting groups complementary to the surface pattern has nicely been illustrated by Muthukumar (Fig. 13.4) [4]. Loop entropy is the reason that the path to the global minimum, i.e. the complex based on correct pattern recognition, does proceed via intermediate stages, which are not the most stable of their kind and hence kinetically less accessible. As a result, the foldamer can readily get ''distracted'', i.e. enter the wrong reaction funnel, and therefore it is essential that all elementary steps are reversible to adopt the lowest energy adsorption conformation.

Was this article helpful?

0 0

Post a comment