System-Size Dependence of Helix-Bundle Formation for Generic Semiflexible Polymers

Abstract

Helical polymer bundles are an important fixture in biomolecular systems. The particular structural geometry of helix bundles is dependent on many factors including the length of the polymer chain. In this study, we performed Monte Carlo simulations of a coarse-grained model for helical polymers to determine the influence of polymer length on tertiary structure formation. Helical structures of semiflexible polymers are analyzed for several chain lengths under thermal conditions. Structural hyperphase diagrams, parametrized by torsion strength and temperature, are constructed and compared.

Single-molecule mechanical unfolding experiments reveal a critical length for the formation of α-helices in peptides

“…Indeed, such helices are known to present a helical critical length similar to the one presented here. 7,[15][16][17][18] We believe that the concept of critical length, previously envisioned by computational studies and hereby confirmed by our experiments, will also have an impact on the design of synthetic molecules made of artificial residues with much more rigid backbones than peptides (like backbones that possess aryl rings in their main chain), 53 in a way to create stable helices of more than 20 units, thus leading to secondary structures with high conformational rigidity and possible unprecedented mechanical properties.…”

“…1d, probing 4 a-helices in series occurs with the lowest probability (19% of the cases). Based on this distribution, we can conclude that most of the time we probe a double-helix bundle that is formed in solution 17,50 (54% of the cases). It is important to note that the breaking of intermolecular interactions within the helix bundles is not detected during our pulling experiments given the very small inter-helix rupture force (and very small length increase) associated with this bundle opening, in agreement with previous force spectroscopy data on triple helix bundles of spectrin.…”

“…In a long polypeptide chain (90 AA) and in a helicogenic solvent, it is not surprising to have a very low probability of observing a single 20 AA helix in solution, mainly due to the stabilizing interaction between two helices as a double-helix bundle. 17 Furthermore, a helix of 20 AA is subjected to an equilibrium between unfolded coiled-coil and folded helical conformations, 7 which decreases the probability to probe it in real-time by AFM. However, when performing pulling-relaxing experiments (discussed below), we could evidence a few plateaus of about 5 nm (= 23 AA).…”

“…This tendency of a long a-helix to adopt a self-folded conformation made of multiple helices in series seems to be dominating for homopolypeptides and other semiflexible polymers. 7,[15][16][17][18] Additionally, the length of intact a-helices in proteins is known to be small, the majority of helical structures being constituted of less than 30 amino acid residues. 19,20 Longer a-helices present a typical kink in their secondary structure.…”

Hybrid polymers bearing oligo-l-lysine(carboxybenzyl)s: synthesis and investigations of secondary structure

“…Additionally, it has been known that the perfectly ordered biologically active threedimensional structures of proteins form such functional assemblies by the interplay of varying interactions, e.g., noncovalent interactions. 64,65 These noncovalent cooperative interactions are mainly interpreted from their hydrogen bonding affinities. 66,67 Similar to our current study model helical polymers, studied under different conditions to examine their helixcoil transitions, also showed changes in secondary structure induced by the repeating number of helical chains, i.e., length and strength of helices.…”