Finite size effects on locating conformational transitions for macromolecules

Effects of macromolecular crowding on the folding of a polymer chain: A Wang-Landau simulation study

A flexible polymer chain in the presence of inert macromolecular crowders will experience a loss of configurational entropy due to the crowder excluded volume. This entropy reduction will be most pronounced in good solvent conditions where the chain assumes an expanded coil conformation. For polymers that undergo a folding transition from a coil to a compact ordered state, as is the case for many globular proteins, macromolecular crowding is expected to stabilize the folded state and thereby shift the transition location. Here, we study such entropic stabilization effects for a tangent square-well sphere chain (monomer diameter σ) in the presence of hard-sphere (HS) crowders (diameter D ≥ σ). We use the Wang-Landau simulation algorithm to construct the density of states for this chain in a crowded environment and are thus able to directly compute the reduction in configurational entropy due to crowding. We study both a chain that undergoes all-or-none folding directly from the coil state and a chain that folds via a collapsed-globule intermediate state. In each case, we find an increase in entropic stabilization for the compact states with an increase in crowder density and, for fixed crowder density, with a decrease in crowder size (concentrated, small crowders have the largest effect). The crowder significantly reduces the average size for the unfolded states while having a minimal effect on the size of the folded states. In the athermal limit, our results directly provide the confinement free energy due to crowding for a HS chain in a HS solvent.

Responsive behavior of a branched-chain polymer network: a molecular dynamics study

Smart polymer hydrogels, which can undergo structural and volume phase transitions in response to external stimuli, have gained much attention for their widespread technological applications. Compared to linear polymers, branched chains offer more extensive opportunities to rationally design functional materials, since they permit more extensive structural tunability-for instance by adjusting the balance between hydrophobic and hydrophilic units, the grafting fraction of backbone monomers, or the side chain length, topology, and solubility. Here we conduct coarse-grained molecular dynamics simulations to assess how well generic physical principles capture this complex interplay of tuning parameters, specifically when building networks from complex branched chains with a hydrophobic backbone. Swollen chains collapse upon reducing side chain solubility, length, and grafting density, but neither the sharpness of this transition nor its dynamic range, if measured via chain extension, depends monotonically on these parameters. Networks comprising such chains are more swollen and exhibit even sharper transitions, but their higher responsiveness goes along with a swelling ratio that falls behind that of single chains.

Generic folding and transition hierarchies for surface adsorption of hydrophobic-polar lattice model proteins

The thermodynamic behavior and structural properties of hydrophobic-polar (HP) lattice proteins interacting with attractive surfaces are studied by means of Wang-Landau sampling. Three benchmark HP sequences (48mer, 67mer, and 103mer) are considered with different types of surfaces, each of which attract either all monomers, only hydrophobic (H) monomers, or only polar (P) monomers, respectively. The diversity of folding behavior in dependence of surface strength is discussed. Analyzing the combined patterns of various structural observables, such as, e.g., the derivatives of the numbers of surface contacts, together with the specific heat, we are able to identify generic categories of folding and transition hierarchies. We also infer a connection between these transition categories and the relative surface strengths, i.e., the ratio of the surface attractive strength to the interchain attraction among H monomers. The validity of our proposed classification scheme is reinforced by the analysis of additional benchmark sequences. We thus believe that the folding hierarchies and identification scheme are generic for HP proteins interacting with attractive surfaces, regardless of chain length, sequence, or surface attraction.

Thermal stability of hydrophobic helical oligomers: a lattice simulation study in explicit water

We investigate the thermal stability of helical hydrophobic oligomers using a three-dimensional, water-explicit lattice model and the Wang-Landau Monte Carlo method. The degree of oligomer helicity is controlled by the parameter ε(mm) < 0, which mimics monomer-monomer hydrogen bond interactions leading to the formation of helical turns in atomistic proteins. We vary |ε(mm)| between 0 and 4.5 kcal/mol and therefore investigate systems ranging from flexible homopolymers (i.e., those with no secondary structure) to helical oligomers that are stable over a broad range of temperatures. We find that systems with |ε(mm)| ≤ 2.0 kcal/mol exhibit a broad thermal unfolding transition at high temperature, leading to an ensemble of random coils. In contrast, the structure of conformations involved in a second, low-temperature, transition is strongly dependent on |ε(mm)|. Weakly helical oligomers are observed when |ε(mm)| ≤ 1.0 kcal/mol and exhibit a low-temperature, cold-unfolding-like transition to an ensemble of strongly water-penetrated globular conformations. For higher |ε(mm)| (1.7 kcal/mol ≤ |ε(mm)| ≤ 2.0 kcal/mol), cold unfolding is suppressed, and the low-temperature conformational transition becomes a "crystallization", in which a "molten" helix is transformed into a defect-free helix. The molten helix preserves ≥50% of the helical contacts observed in the "crystal" at a lower temperature. When |ε(mm)| = 4.5 kcal/mol, we find that conformational transitions are largely suppressed within the range of temperatures investigated.

Thermal and structural stability of adsorbed proteins

Experimental evidence suggests that proteins adsorbed to hydrophobic surfaces at low coverages are stabilized relative to the bulk. For larger coverages, proteins unfold and form beta-sheets. We performed computer simulations on model proteins and found that: 1), For weakly adsorbing surfaces, unfolded conformations lose more entropy upon adsorption than folded ones. 2), The melting temperature, both in the bulk and at surfaces, decreases with increasing protein concentration because of favorable interprotein interactions. 3), Proteins in the bulk show large unfolding free energy barriers; this barrier decreases at stronger adsorbing surfaces. We conjecture that typical experimental temperatures appear to be below the bulk melting temperature for a single protein, but above the melting temperature for concentrated protein solutions. Purely thermodynamic factors then explain protein stabilization on adsorption at low concentrations. However, both thermodynamic and kinetic factors are important at higher concentrations. Thus, proteins in the bulk do not denature with increasing concentration due to large kinetic barriers, even though the aggregated state is thermodynamically preferred. However, they readily unfold upon adsorption, with the surface acting as a heterogeneous catalyst. The thermal behavior of proteins adsorbed to hydrophobic surfaces thus appears to follow behavior independent of their chemical specificity.

Conformational transitions of adsorbed proteins on surfaces of varying polarity

Combining a wide range of protein adsorption experiments (three globular proteins on eight well-defined homogeneous surfaces) with Monte Carlo simulations of lattice proteins at different concentrations and on surfaces of varying "polarity", we explore the extent and rheological behavior of adsorbed proteins as a function of substrate polarity, "on" rate constants (k(a)) and steric parameters (|A(1)|) from the random sequential adsorption model, and demonstrate a folding to unfolding transition upon adsorption. We show that model globular proteins (hen egg lysozyme, ribonuclease A, and insulin dimer) behave similarly with respect to adsorption. Experimentally, above a substrate wettability cos theta > 0.4 (where theta is the sessile contact angle of water on a substrate in air), the adsorbed mass, rigidity, and k(a) of the proteins are diminished, while the steric factor |A(1)| is increased, suggesting a lower packing density. To analyze these results, we have invoked computer simulations. We show that changing surface polarity has two profound effects. First, the amount adsorbed increases as the surfaces become more apolar. Further, the proteins become less stable as their adsorbed amount increased because they gain a large number of interprotein and protein-surface interactions. Finally, apolar surfaces served to reduce the unfolding free energy barriers, further facilitating the reorganizing of proteins on these surfaces. Thus, increasing the nonpolar nature of the surfaces resulted in a more rigid adsorbed layer, in good agreement with the experiments.