Enhanced Wang Landau sampling of adsorbed protein conformations

Predicting non-equilibrium folding behavior of polymer chains using the steepest-entropy-ascent quantum thermodynamic framework

The steepest-entropy-ascent quantum thermodynamic (SEAQT) framework is used to explore the influence of heating and cooling on polymer chain folding kinetics. The framework predicts how a chain moves from an initial non-equilibrium state to stable equilibrium along a unique thermodynamic path. The thermodynamic state is expressed by occupation probabilities corresponding to the levels of a discrete energy landscape. The landscape is generated using the Replica Exchange Wang-Landau method applied to a polymer chain represented by a sequence of hydrophobic and polar monomers with a simple hydrophobic-polar amino acid model. The chain conformation evolves as energy shifts among the levels of the energy landscape according to the principle of steepest entropy ascent. This principle is implemented via the SEAQT equation of motion. The SEAQT framework has the benefit of providing insight into structural properties under non-equilibrium conditions. Chain conformations during heating and cooling change continuously without sharp transitions in morphology. The changes are more drastic along non-equilibrium paths than along quasi-equilibrium paths. The SEAQT-predicted kinetics are fitted to rates associated with the experimental intensity profiles of cytochrome c protein folding with Rouse dynamics.

Advancing Rational Control of Peptide-Surface Complexes

Understanding peptide-surface interactions is crucial for programming self-assembly of peptides at surfaces and in realizing their applications, such as biosensors and biomimetic materials. In this study, we developed insights into the dependence of a residue's interaction with a surface on its neighboring residue in a tripeptide using molecular dynamics simulations. This knowledge is integral for designing rational mutations to control peptide-surface complexes. Using graphene as our model surface, we estimated the free energy of adsorption (ΔA_ads) and extracted predominant conformations of 26 tripeptides with the motif LNR-CR-Gly, where LNR and CR are variable left-neighboring and central residues, respectively. We considered a combination of strongly adsorbing (Phe, Trp, and Arg) and weakly adsorbing (Ala, Val, Leu, Ser, and Thr) amino acids on graphene identified in a prior study to form the tripeptides. Our results indicate that ΔA_ads of a tripeptide cannot be estimated as the sum of ΔA_ads of each residue indicating that the residues in a tripeptide do not behave as independent entities. We observed that the contributions from the strongly adsorbing amino acids were dominant, which suggests that such residues could be used for strengthening peptide-graphene interactions irrespective of their neighboring residues. In contrast, the adsorption of weakly adsorbing central residues is dependent on their neighboring residues. Our structural analysis revealed that the dihedral angles of LNR are more correlated with that of CR in the adsorbed state than in bulk state. Together with ΔA_ads trends, this implies that different backbone structures of a given CR can be accessed for a similar ΔA_ads by varying the LNR. Therefore, incorporation of context effects in designing mutations can lead to desired peptide structure at surfaces. Our results also emphasize that these cooperative effects in ΔA_ads and structure are not easily predicted a priori. The collective results have applications in guiding rational mutagenesis techniques to control orientation of peptides at surfaces and in developing peptide structure prediction algorithms in adsorbed state from its sequence.

Elucidating thermal behavior, native contacts, and folding funnels of simple lattice proteins using replica exchange Wang-Landau sampling

We studied the folding behavior of two coarse-grained, lattice models, the HP (hydrophobic-polar) model and the semi-flexible H0P model, whose 124 monomer long sequences were derived from the protein Ribonuclease A. Taking advantage of advanced parallel computing techniques, we applied replica exchange Wang-Landau sampling and calculated the density of states over the models entire energy ranges to high accuracy. We then determined both energetic and structural quantities in order to elucidate the folding behavior of each model completely. As a result of sufficiently long sequences and model complexity, yet computational accessibility, we were able to depict distinct free energy folding funnels for both models. In particular, we found that the HP model folds in a single-step process with a very highly degenerate native state and relatively flat low temperature folding funnel minimum. By contrast, the semi-flexible H0P model folds via a multi-step process and the native state is almost four orders of magnitude less degenerate than that for the HP model. In addition, for the H0P model, the bottom of the free energy folding funnel remains rough, even at low temperatures.

The role of chain-stiffness in lattice protein models: A replica-exchange Wang-Landau study

Using Monte Carlo simulations, we investigate simple, physically motivated extensions to the hydrophobic-polar lattice protein model for the small (46 amino acid) protein Crambin. We use two-dimensional replica-exchange Wang-Landau sampling to study the effects of a bond angle stiffness parameter on the folding and uncover a new step in the collapse process for particular values of this stiffness parameter. A physical interpretation of the folding is developed by analysis of changes in structural quantities, and the free energy landscape is explored. For these special values of stiffness, we find non-degenerate ground states, a property that is consistent with behavior of real proteins, and we use these unique ground states to elucidate the formation of native contacts during the folding process. Through this analysis, we conclude that chain-stiffness is particularly influential in the low energy, low temperature regime of the folding process once the lattice protein has partially collapsed.

Interplay of Coil-Globule Transition and Surface Adsorption of a Lattice HP Protein Model

An end-grafted hydrophobic-polar (HP) model protein chain with alternating H and P monomers is studied to examine interactions between the critical adsorption transition due to surface attraction and the collapse transition due to pairwise attractive H–H interactions. We find that the critical adsorption phenomenon can always be observed; however, the critical adsorption temperature T_CAP is influenced by the attractive H–H interactions in some cases. When the collapse temperature T_c is lower than T_CAP, the critical adsorption of the HP chain is similar to that of a homopolymer without intrachain attractions and T_CAP remains unchanged, whereas the collapse transition is suppressed by the adsorption. In contrast, for cases where T_c is close to or higher than T_CAP, T_CAP of the HP chain is increased, indicating that a collapsed chain is more easily adsorbed on the surface. The strength of the H–H attraction also influences the statistical size and shape of the polymer, with strong H–H attractions resulting in adsorbed and collapsed chains adopting two-dimensional, circular conformations.

Effect of single-site mutations on hydrophobic-polar lattice proteins

We developed a heuristic method for determining the ground-state degeneracy of hydrophobic-polar (HP) lattice proteins, based on Wang-Landau and multicanonical sampling. It is applied during comprehensive studies of single-site mutations in specific HP proteins with different sequences. The effects in which we are interested include structural changes in ground states, changes of ground-state energy, degeneracy, and thermodynamic properties of the system. With respect to mutations, both extremely sensitive and insensitive positions in the HP sequence have been found. That is, ground-state energies and degeneracies, as well as other thermodynamic and structural quantities, may be either largely unaffected or may change significantly due to mutation.

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.

Selective adsorption of lattice peptides on patterned surfaces

To study the adsorption of individual peptides in implicit solvent, we propose a version of the Wang-Landau Monte Carlo algorithm that uses a single surface, with no need for a confining wall or grafting. Our "wall-free" method is both more efficient than the traditional ones and free of additional assumptions or approximations. We illustrate it by simulating an HP-model lattice peptide on planar surfaces with a variety of patterns of adsorption sites, discovering a temperature-induced switch of surface selection which is due to a balance of energetic and entropic effects.