How does the coupling of secondary and tertiary interactions control the folding of helical macromolecules?

Abstract

The authors study how the simultaneous presence of short-range secondary and long-range tertiary interactions controls the folding and collapse behavior of a helical macromolecule. The secondary interactions stabilize the helical conformation of the chain, while the tertiary interactions govern its overall three-dimensional shape. The authors have carried out Monte Carlo simulations to study the effect of chain length on the folding and collapse behavior of the chain. They have calculated state diagrams for four chain lengths and found that the physics is very rich with a plethora of stable conformational states. In addition to the helix-coil and coil-globule transitions, their model describes the coupling between them which takes place at low temperatures. Under these conditions, their model predicts a cascade of continuous, conformational transitions between states with an increase in the strength of the tertiary interactions. During each transition the chain shrinks, i.e., collapses, in a rapid and specific manner. In addition, the number of the transitions increases with increasing chain length. They have also found that the low-temperature regions of the state diagram between the transition lines cannot be associated with specific structures of the chain, but rather, with ensembles of various configurations of the chain with similar characteristics. Based on these results the authors propose a mechanism for the folding and collapse of helical macromolecules which is further supported by the analysis of configurational, configurational, and thermodynamic properties of the chain.

Minimal Model of Intrinsic Chirality to Study the Folding Behavior of Helical Polymers

“…In contrast, in poor solvent characterized by a significant long-range attraction between chain residues, the above helix–coil transformation is superimposed by a sharp discontinuous helix–globule collapse in the low-mid temperature range. On the basis of the data for the average chain potential energy, its radius of gyration, and the specific heat, as functions of temperature, we suggest that this transformation resembles a thermodynamic phase transition driven by thermal fluctuations, which is supported by previous experimental data, numerical simulations, and the theory of semiflexible polymers. ,,, Conformational intermediates captured during the helix–globule collapse indicate that it proceeds via nucleation initiated at the polymer termini, so that the chain subsequently collapses into the globule alongside its axis. This process is reminiscent of the Halperin–Goldbart mechanism, , whereby sufficiently flexible polymer chains collapse into terminal “raindrops” in the short-chain limit.…”

“…This model demonstrates that helix foldability may increase with anisotropy in the potential function, and undergoes discontinuous first-order-like helix–coil transitions. , Varshney et al have taken a similar approach, and utilized a dihedral angle cutoff to assign individual beads a negative enthalpy, thereby emulating formation of a hydrogen bond . They find a rich state diagram where continuous helix–coil and coil–globule transitions become coupled at low temperature and sufficient particle interaction strength ε . While both models consider torsional angles between individual residues a basis for helicity, they do not implement true intrinsic curvature κ and torsion τ, as represented in the Yamakawa theory .…”

Microscopic formulation of the Zimm-Bragg model for the helix-coil transition

“…At the same time, interpretations of results from single-molecule techniques, such as stretching with optical tweezers [7], have largely relied on applications of classical spin models [8]. In addition these spin approaches remain attractive for describing folding of helical proteins [9] and influences of solvent on secondary structure formation and stability [10]. Among these, the Zimm-Bragg (ZB) model stands out for its success [11].…”

Pendent polyimides using mellitic acid dianhydride. III. The effect of pendent group functionality on polymer properties

“…Understanding and controlling polymer chain interactions continues to be of fundamental importance in polymer science. Some of the relevant parameters investigated previously include polymer molecular weight,1, 2 temperature and solvent control of chain conformation,3–9 the addition of ancillary polymers (blends) or small molecules,10–15 main chain structural features (e.g., spiro structure,16 pattern of ring substitution,17 and block copolymer interactions18, 19), degree of hydrogenation,20 functionalization of endgroups (for design of supramolecular architectures),21 and attachment/grafting of side groups onto polymer chains 4, 22–48…”