Anders Irbäck

Oligomerization of Amyloid Aβ16–22 Peptides Using Hydrogen Bonds and Hydrophobicity Forces

The 16-22 amino-acid fragment of the beta-amyloid peptide associated with the Alzheimers disease, Abeta, is capable of forming amyloid fibrils. Here we study the aggregation mechanism of Abeta16-22 peptides by unbiased thermodynamic simulations at the atomic level for systems of one, three, and six Abeta16-22 peptides. We find that the isolated Abeta16-22 peptide is mainly a random coil in the sense that both the alpha-helix and beta-strand contents are low, whereas the three- and six-chain systems form aggregated structures with a high beta-sheet content. Furthermore, in agreement with experiments on Abeta16-22 fibrils, we find that large parallel beta-sheets are unlikely to form. For the six-chain system, the aggregated structures can have many different shapes, but certain particularly stable shapes can be identified.

STUDIES OF AN OFF-LATTICE MODEL FOR PROTEIN FOLDING: SEQUENCE DEPENDENCE AND IMPROVED SAMPLING AT FINITE TEMPERATURE

We study the thermodynamic behavior of a simple off‐lattice model for protein folding. The model is two dimensional and has two different ‘‘amino acids.’’ Using numerical simulations of all chains containing eight or ten monomers, we examine the sequence dependence at a fixed temperature. It is shown that only a few of the chains exist in unique folded state at this temperature, and the energy level spectra of chains with different types of behavior are compared. Furthermore, we use this model as a testbed for two improved Monte Carlo algorithms. Both algorithms are based on letting some parameter of the model become a dynamical variable; one of the algorithms uses a fluctuating temperature and the other a fluctuating monomer sequence. We find that by these algorithms one gains large factors in efficiency in comparison with conventional methods.

Monte Carlo update for chain molecules: Biased Gaussian steps in torsional space

We develop a new elementary move for simulations of polymer chains in torsion angle space. The method is flexible and easy to implement. Tentative updates are drawn from a (conformation-dependent) Gaussian distribution that favors approximately local deformations of the chain. The degree of bias is controlled by a parameter b. The method is tested on a reduced model protein with 54 amino acids and the Ramachandran torsion angles as its only degrees of freedom, for different b. Without excessive fine tuning, we find that the effective step size can be increased by a factor of 3 compared to the unbiased b=0 case. The method may be useful for kinetic studies, too.

Three-helix-bundle protein in a Ramachandran model

We study the thermodynamic behavior of a model protein with 54 amino acids that forms a three-helix bundle in its native state. The model contains three types of amino acids and five to six atoms per amino acid and has the Ramachandran torsional angles phi(i), psi(i) as its degrees of freedom. The force field is based on hydrogen bonds and effective hydrophobicity forces. For a suitable choice of the relative strength of these interactions, we find that the three-helix-bundle protein undergoes an abrupt folding transition from an expanded state to the native state. Also shown is that the corresponding one- and two-helix segments are less stable than the three-helix sequence.

PROFASI: A Monte Carlo simulation package for protein folding and aggregation†

We present a flexible and efficient program package written in C++, PROFASI, for simulating protein folding and aggregation. The systems are modeled using an all‐atom description of the protein chains with only torsional degrees of freedom, and implicit water. The program package has a modular structure that makes the interaction potential easy to modify. The currently implemented potential is able to fold several peptides with about 20 residues, and has also been used to study aggregation and force‐induced unfolding. The simulation methods implemented in PROFASI are Monte Carlo‐based and include a semilocal move and simulated tempering. Adding new updates is easy. The code runs fast in both single‐ and multi‐chain applications, as is illustrated by several examples.

Local interactions and protein folding : A three-dimensional off-lattice approach

The thermodynamic behavior of a three-dimensional off-lattice model for protein folding is probed. The model has only two types of residues, hydrophobic and hydrophilic. In absence of local interactions, native structure formation does not occur for the temperatures considered. By including sequence independent local interactions, which qualitatively reproduce local properties of functional proteins, the dominance of a native state for many sequences is observed. As in lattice model approaches, folding takes place by gradual compactification, followed by a sequence dependent folding transition. Our results differ from lattice approaches in that bimodal energy distributions are not observed and that high folding temperatures are accompanied by relatively low temperatures for the peak of the specific heat. Also, in contrast to earlier studies using lattice models, our results convincingly demonstrate that one does not need more than two types of residues to generate sequences with good thermodynamic folding...

Formation and Growth of Oligomers: A Monte Carlo Study of an Amyloid Tau Fragment

Small oligomers formed early in the process of amyloid fibril formation may be the major toxic species in Alzheimers disease. We investigate the early stages of amyloid aggregation for the tau fragment AcPHF6 (Ac-VQIVYK-NH2) using an implicit solvent all-atom model and extensive Monte Carlo simulations of 12, 24, and 36 chains. A variety of small metastable aggregates form and dissolve until an aggregate of a critical size and conformation arises. However, the stable oligomers, which are β-sheet-rich and feature many hydrophobic contacts, are not always growth-ready. The simulations indicate instead that these supercritical oligomers spend a lengthy period in equilibrium in which considerable reorganization takes place accompanied by exchange of chains with the solution. Growth competence of the stable oligomers correlates with the alignment of the strands in the β-sheets. The larger aggregates seen in our simulations are all composed of two twisted β-sheets, packed against each other with hydrophobic side chains at the sheet–sheet interface. These β-sandwiches show similarities with the proposed steric zipper structure for PHF6 fibrils but have a mixed parallel/antiparallel β-strand organization as opposed to the parallel organization found in experiments on fibrils. Interestingly, we find that the fraction of parallel β-sheet structure increases with aggregate size. We speculate that the reorganization of the β-sheets into parallel ones is an important rate-limiting step in the formation of PHF6 fibrils.

Folding of a small helical protein using hydrogen bonds and hydrophobicity forces

A reduced protein model with five to six atoms per amino acid and five amino acid types is developed and tested on a three‐helix‐bundle protein, a 46‐amino acid fragment from staphylococcal protein A. The model does not rely on the widely used Gō approximation, which ignores non‐native interactions. We find that the collapse transition is considerably more abrupt for the protein A sequence than for random sequences with the same composition. The chain collapse is found to be at least as fast as helix formation. Energy minimization restricted to the thermodynamically favored topology gives a structure that has a root‐mean‐square deviation of 1.8 Å from the native structure. The sequence‐dependent part of our potential is pairwise additive. Our calculations suggest that fine‐tuning this potential by parameter optimization is of limited use. Proteins 2002;47:99–105.

Folding Thermodynamics of Peptides

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.

Enumerating Designing Sequences in the HP Model

The hydrophobic/polar HP model on the square lattice has been widely used toinvestigate basics of protein folding. In the cases where all designing sequences (sequences with unique ground states) were enumerated without restrictions on the number of contacts, the upper limit on the chain length N has been 18–20 because of the rapid exponential growth of thenumbers of conformations and sequences. We show how a few optimizations push this limit by about 5 units. Based on these calculations, we study the statistical distribution of hydrophobicity along designing sequences. We find that the average number of hydrophobic and polar clumps along the chains is larger for designing sequences than for random ones, which is in agreement with earlier findings for N ≤ 18 and with results for real enzymes. We also show that this deviation from randomness disappears if the calculations are restricted to maximally compact structures.