ß-Hairpin Crowding Agents Affect α-Helix Stability in Crowded Environments.

The dense, heterogeneous cellular environment is known to affect protein stability. It is now recognized that attractive "quinary" interactions with other biomacromolecules in the cell, referred to as the crowding agents, play a significant role in determining the stability of the protein of interest or test protein. These attractive interactions can reduce or overcome the stabilizing effect of the excluded volume of the crowding agents. However, the roles of specific interactions, such as hydrogen bonding and side chain-side chain hydrophobic interactions, are still unclear. Here, we use molecular simulation to investigate the roles played by hydrophobic interactions and hydrogen bonding between a small helical test protein and equally sized crowding agent proteins in a fixed ß-hairpin configuration. The test protein and crowding agents are represented by a coarse-grained protein model, and we use multicanonical molecular dynamics to study the folding thermodynamics of the test protein. Our results confirm that the stability of the test protein depends on the hydrophobicity of the crowding agents and that the stability of the test protein is reduced through favorable side chain-side chain interactions that preferentially stabilize the unfolded states. In addition, we show that when the intermolecular hydrophobic interactions are more favorable than the intramolecular hydrophobic interactions, the ß-rich crowding agents can completely destabilize the test protein, causing it to adopt configurations with increased ß-content and preventing it from forming its native helical state. Similarities between our results and those seen in the formation of amyloid fibrils are also discussed.

Protein-protein interactions affect alpha helix stability in crowded environments.

The dense, heterogeneous cellular environment is known to affect protein stability through interactions with other biomacromolecules. The effect of excluded volume due to these biomolecules, also known as crowding agents, on a protein of interest, or test protein, has long been known to increase the stability of a test protein. Recently, it has been recognized that attractive protein-crowder interactions play an important role. These interactions affect protein stability and can destabilize the test protein. However, most computational work investigating the role of attractive interactions has used spherical crowding agents and has neglected the specific roles of crowding agent hydrophobicity and hydrogen bonding. Here we use multicanonical molecular dynamics and a coarse-grained protein model to study the folding thermodynamics of a small helical test protein in the presence of crowding agents that are themselves proteins. Our results show that the stability of the test protein depends on the hydrophobicity of the crowding agents. For low values of crowding agent hydrophobicity, the excluded volume effect is dominant, and the test protein is stabilized relative to the dilute solution. For intermediate values of the crowding agent hydrophobicity, the test protein is destabilized by favorable side chain-side chain interactions stabilizing the unfolded states. For high values of the crowding agent hydrophobicity, the native state is stabilized by the strong intermolecular attractions, causing the formation of a packed structure that increases the stability of the test protein through favorable side chain-side chain interactions. In addition, increasing crowding agent hydrophobicity increases the "foldability" of the test protein and alters the potential energy landscape by simultaneously deepening the basins corresponding to the folded and unfolded states and increasing the energy barrier between them.

Density functional theory of a curved liquid-vapour interface: evaluation of the rigidity constants.

It is argued that to arrive at a quantitative description of the surface tension of a liquid drop as a function of its inverse radius, it is necessary to include the bending rigidity k and Gaussian rigidity k in its description. New formulae for k and k in the context of density functional theory with a non-local, integral expression for the interaction between molecules are presented. These expressions are used to investigate the influence of the choice of Gibbs dividing surface, and it is shown that for a one-component system, the equimolar surface has a special status in the sense that both k and k are then the least sensitive to a change in the location of the dividing surface. Furthermore, the equimolar value for k corresponds to its maximum value and the equimolar value for k corresponds to its minimum value. An explicit evaluation using a short-ranged interaction potential between molecules shows that k is negative with a value around minus 0.5-1.0 kBT and that k is positive with a value that is a bit more than half the magnitude of k. Finally, for dispersion forces between molecules, we show that a term proportional to log(R)/R(2) replaces the rigidity constants and we determine the (universal) proportionality constants.

Thermodynamics of peptide dimer formation.

The Replica Exchange Statistical Temperature Molecular Dynamics algorithm is used to study the equilibrium properties of a peptide monomer and dimer and the thermodynamics of peptide dimer formation. The simulation data are analyzed by the Statistical Temperature Weighted Histogram Analysis Method. Each 10-residue peptide is represented by a coarse-grained model with hydrophobic side chains and has an α-helix as its minimum energy configuration. It is shown that the configurational behavior of the dimer can be divided into four regions as the temperature increases: two folded peptides; one folded and one unfolded peptide; two unfolded peptides; and two spatially separated peptides. Two important phenomena are discussed: in the dimer, one peptide unfolds at a lower temperature than the isolated monomer and the other peptide unfolds at a higher temperature than the isolated monomer. In addition, in the temperature region where one peptide is folded and the other unfolded, the unfolded peptide adopts an extended structure that minimizes the overall surface area of the aggregate. It is suggested that combination of destabilization due to aggregation and the resulting extended configuration of the destabilized peptide could have implications for nucleating ß-sheet structures and the ultimate formation of fibrils.

Direct determination of the Tolman length from the bulk pressures of liquid drops via molecular dynamics simulations.

An expression for the difference in pressure between a liquid drop in equilibrium with its vapor Deltap=p([script-l])-p(v) is derived from previous expressions for the components of the Irving-Kirkwood pressure tensor. This expression, as well as the bulk values of the pressure tensor, is then evaluated via molecular dynamics simulations of particles interacting through a truncated Lennard-Jones potential. We determine the Tolman length delta from the dependence of Deltap on the equimolar radius. We determine the Tolman length to be delta=-0.10+/-0.02 in units of the particle diameter. This is the first determination of the Tolman length for liquid droplets via the pressure tensor route through computer simulation that is negative, in contrast to all previous results from simulation, but in agreement with results from density functional theory. In addition, we study the planar liquid-vapor interface and observe a dependence of the physical properties of the system on the system size, as measured by the surface area.

Coarse-Grained Model of Coil-to-Helix Kinetics Demonstrates the Importance of Multiple Nucleation Sites in Helix Folding.

An extension of a coarse-grained, implicit-solvent peptide model wherein each amino acid residue is represented by four interaction sites is presented and discussed. The model is used to study the coil-to-helix transition of five peptide sequences, ranging from all hydrophobic to all hydrophilic, for a 10-residue peptide. The thermodynamics of the folding transition are analyzed and discussed for each sequence, and the stability of the α-helix is correlated with the hydrophobic content of the sequence. In addition, for each sequence, the folding kinetics of the transition from random coil to full α-helix are analyzed, and the mean folding time is determined. Folding times vary from 59 ns for the most hydrophobic sequence to 132 ns for the most hydrophilic sequence. These folding times compare very well with those measured in experments. All sequences show single-exponential kinetics. A plot of the mean folding time versus the reciprocal of the Zimm-Bragg parameter σ [Formula: see text] a measure of the free energy cost of nucleating a helix [Formula: see text] is shown to be nonlinear, in contrast to the predictions of many theories of the coil-to-helix transition. It is proposed that the origin of this nonlinearity is due to multiple helix nucleation sites, indicating that even for short peptides such as those studied here, multiple folding pathways play an important role in the transition from random coil to native state.

Monte Carlo simulations of polyalanine using a reduced model and statistics-based interaction potentials.

A coarse-grained residue-residue interaction potential derived from a statistical analysis of the Protein Data Bank is used to investigate the coil-to-helix transition for polyalanine. The interaction potentials depend on the radial distance between interaction sites, as well as the relative orientation of the sites. Two types of interaction sites are present in the model: a site representing the amino acid side chain, and a site representing a "virtual backbone," i.e., a site located in the peptide bond which accounts for backbone hydrogen bonding. Two chain lengths are studied and the results for the thermodynamics of the coil-to-helix transition are analyzed in terms of the Zimm-Bragg model. Results agree qualitatively and quantitatively with all-atom Monte Carlo simulations and other reduced-model Monte Carlo simulations.