Effects of Confinement on the Thermodynamics of a Collapsing Heteropolymer: An Off-Lattice Wang−Landau Monte Carlo Simulation Study

All-or-none folding of a flexible polymer chain in cylindrical nanoconfinement

Geometric confinement of a polymer chain results in a loss of conformational entropy. For a chain that can fold into a compact native state via a first-order-like transition, as is the case for many small proteins, confinement typically provides an entropic stabilization of the folded state, thereby shifting the location of the transition. This allows for the possibility of confinement (entropy) driven folding. Here, we investigate such confinement effects for a flexible square-well-sphere N-mer chain (monomer diameter σ) confined within a long cylindrical pore (diameter D) or a closed cylindrical box (height H = D). We carry out Wang-Landau simulations to construct the density of states, which provides access to the complete thermodynamics of the system. For a wide pore, an entropic stabilization of the folded state is observed. However, as the pore diameter approaches the size of the folded chain (D ∼ N^1/3σ), we find a destabilization effect. For pore diameters smaller than the native ground-state, the chain folds into a different, higher energy, ground state ensemble and the T vs D phase diagram displays non-monotonic behavior as the system is forced into different ground states for different ranges of D. In this regime, isothermal reduction of the confinement dimension can induce folding, unfolding, or crystallite restructuring. For the cylindrical box, we find a monotonic stabilization effect with decreasing D. Scaling laws for the confinement free energy in the athermal limit are also investigated.

Reaching new levels of realism in modeling biological macromolecules in cellular environments

An increasing number of studies are aimed at modeling cellular environments in a comprehensive and realistic fashion. A major challenge in these efforts is how to bridge spatial and temporal scales over many orders of magnitude. Furthermore, there are additional challenges in integrating different aspects ranging from questions about biomolecular stability in crowded environments to the description of reactive processes on cellular scales. In this review, recent studies with models of biomolecules in cellular environments at different levels of detail are discussed in terms of their strengths and weaknesses. In particular, atomistic models, implicit representations of cellular environments, coarse-grained and spheroidal models of biomolecules, as well as the inclusion of reactive processes via reaction-diffusion models are described. Furthermore, strategies for integrating the different models into a comprehensive description of cellular environments are discussed.

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

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.