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We use Markov state models (MSMs) to analyze the dynamics of a β-hairpin-forming peptide in Monte Carlo (MC) simulations with interacting protein crowders, for two different types of crowder proteins [bovine pancreatic trypsin inhibitor (BPTI) and GB1]. In these systems, at the temperature used, the peptide can be folded or unfolded and bound or unbound to crowder molecules. Four or five major free-energy minima can be identified. To estimate the dominant MC relaxation times of the peptide, we build MSMs using a range of different time resolutions or lag times. We show that stable relaxation-time estimates can be obtained from the MSM eigenfunctions through fits to autocorrelation data. The eigenfunctions remain sufficiently accurate to permit stable relaxation-time estimation down to small lag times, at which point simple estimates based on the corresponding eigenvalues have large systematic uncertainties. The presence of the crowders has a stabilizing effect on the peptide, especially with BPTI crowders, which can be attributed to a reduced unfolding rate k u , while the folding rate k f is left largely unchanged.

Using Monte Carlo methods, we explore and compare the effects of two protein crowders, BPTI and GB1, on the folding thermodynamics of two peptides, the compact helical trp-cage and the β-hairpin-forming GB1m3. The thermally highly stable crowder proteins are modeled using a fixed backbone and rotatable side-chains, whereas the peptides are free to fold and unfold. In the simulations, the crowder proteins tend to distort the trp-cage fold, while having a stabilizing effect on GB1m3. The extent of the effects on a given peptide depends on the crowder type. Due to a sticky patch on its surface, BPTI causes larger changes than GB1 in the melting properties of the peptides. The observed effects on the peptides stem largely from attractive and specific interactions with the crowder surfaces, and differ from those seen in reference simulations with purely steric crowder particles.

While steric crowders tend to stabilize globular proteins, it has been found that protein crowders can have an either stabilizing or destabilizing effect, where a destabilization may arise from nonspecific attractive interactions between the test protein and the crowders. Here, we use Monte Carlo replica-exchange methods to explore the equilibrium behavior of the miniprotein trp-cage in the presence of protein crowders. Our results suggest that the surrounding crowders prevent trp-cage from adopting its global native fold, while giving rise to a stabilization of its main secondary-structure element, an α-helix. With the crowding agent used (bovine pancreatic trypsin inhibitor), the trp-cage-crowder interactions are found to be specific, involving a few key residues, most of which are prolines. The effects of these crowders are contrasted with those of hard-sphere crowders.

Using all-atom Monte Carlo simulations with implicit water, combined with a cluster size analysis, we study the aggregation of Abeta(16) (-22), a peptide capable of forming amyloid fibrils. We consider a system of six initially randomly oriented Abeta(16) (-22) peptides, and investigate the thermodynamics and structural properties of aggregates formed by this system. The system is unaggregated without ordered secondary structure at high temperature, and forms beta-sheet rich aggregates at low temperature. At the crossover between these two regimes, we find that clusters of all sizes occur, whereas the beta-strand content is low. In one of several runs, we observe the spontaneous formation of a beta-barrel with six antiparallel strands. The beta-barrel stands out as the by far most long-lived aggregate seen in our simulations., ((c) 2007 Wiley-Liss, Inc.)

Recent experiments have identified peptides that adhere to GaAs and Si surfaces. Here, we use all-atom Monte Carlo simulations with implicit solvent to investigate the behavior in aqueous solution of four such peptides, all with 12 residues. At room temperature, we find that all four peptides are largely unstructured, which is consistent with experimental data. At the same time, we find that one of the peptides is structurally different and more flexible, as compared to the others. This finding points at structural differences as a possible explanation for differences in adhesion properties among these peptides. By also analyzing designed mutants of two of the peptides, an experimental test of this hypothesis is proposed.

A simplified interaction potential for protein folding studies at the atomic level is discussed and tested on a set of peptides with approximately 20 residues each. The test set contains both alpha-helical (Trp cage, F(s)) and beta-sheet (GB1p, GB1m2, GB1m3, Betanova, LLM) peptides. The model, which is entirely sequence-based, is able to fold these different peptides for one and the same choice of model parameters. Furthermore, the melting behavior of the peptides is in good quantitative agreement with experimental data. Apparent folded populations obtained using different observables are compared, and are found to be very different for some of the peptides (e.g., Betanova). In other cases (in particular, GB1m2 and GB1m3), the different estimates agree reasonably well, indicating a more two-state-like melting behavior.

We study the folding thermodynamics of a beta-hairpin and two three-stranded beta-sheet peptides using a simplified sequence-based all-atom model, in which folding is driven mainly by backbone hydrogen bonding and effective hydrophobic attraction. The native populations obtained for these three sequences are in good agreement with experimental data. We also show that the apparent native population depends on which observable is studied; the hydrophobicity energy and the number of native hydrogen bonds give different results. The magnitude of this dependence matches well with the results obtained in two different experiments on the beta-hairpin., (Copyright 2004 Wiley-Liss, Inc.)

The Hybrid Monte Carlo method offers a rigorous and potentially efficient approach to the simulation of dense systems, by combining numerical integration of Newton's equations of motion with a Metropolis accept-or-reject step. The Metropolis step corrects for sampling errors caused by the discretization of the equations of motion. The integration is usually performed using a uniform step size. Here, we present simulations of the Lennard-Jones system showing that the use of smaller time steps in the tails of each integration trajectory can reduce errors in energy. The acceptance rate is 10-15 percentage points higher in these runs, compared to simulations with the same trajectory length and the same number of integration steps but a uniform step size. We observe similar effects for the harmonic oscillator and a coarse-grained peptide model, indicating generality of the approach. [ABSTRACT FROM AUTHOR]

Recent years have seen an increasing number of biophysical studies of proteins being conducted in cells and concentrated protein solutions. In these experiments, compared to dilute-solution data, both stabilization and destabilization of globular proteins have been observed, which cannot be explained in terms of volume exclusion alone. For a fundamental understanding of the observed effects, there is a need for computational modeling beyond the level of hard-sphere crowders. This mini-review discusses recent efforts to simulate folding/unfolding properties of proteins in the presence of explicit macromolecular crowders. A Monte Carlo-based approach by us is described, which we recently applied to study the equilibrium folding thermodynamics of two peptides in the presence of explicit protein crowders. [ABSTRACT FROM AUTHOR]

We present and study a minimal structure-based model for the self-assembly of peptides into ordered β-sheet-rich fibrils. The peptides are represented by unit-length sticks on a cubic lattice and interact by hydrogen bonding and hydrophobicity forces. Using Monte Carlo simulations with > 105 peptides, we show that fibril formation occurs with sigmoidal kinetics in the model. To determine the mechanism of fibril nucleation, we compute the joint distribution in length and width of the aggregates at equilibrium, using an efficient cluster move and flat-histogram techniques. This analysis, based on simulations with 256 peptides in which aggregates form and dissolve reversibly, shows that the main free-energy barriers that a nascent fibril has to overcome are associated with changes in width. [ABSTRACT FROM AUTHOR]