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 >10(5) 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.

Amyloid β-protein (Aβ) sequence length variants with varying aggregation propensity coexist in vivo, where coaggregation and cross-catalysis phenomena may affect the aggregation process. Until recently, naturally occurring amyloid β-protein (Aβ) variants were believed to begin at or after the canonical β-secretase cleavage site within the amyloid β-protein precursor. However, N-terminally extended forms of Aβ (NTE-Aβ) were recently discovered and may contribute to Alzheimer's disease. Here, we have used thioflavin T fluorescence to study the aggregation kinetics of Aβ42 variants with N-terminal extensions of 5–40 residues, and transmission electron microscopy to analyze the end states. We find that all variants form amyloid fibrils of similar morphology as Aβ42, but the half-time of aggregation (t1/2) increases exponentially with extension length. Monte Carlo simulations of model peptides suggest that the retardation is due to an underlying general physicochemical effect involving reduced frequency of productive molecular encounters. Indeed, global kinetic analyses reveal that NTE-Aβ42s form fibrils via the same mechanism as Aβ42, but all microscopic rate constants (primary and secondary nucleation, elongation) are reduced for the N-terminally extended variants. Still, Aβ42 and NTE-Aβ42 coaggregate to form mixed fibrils and fibrils of either Aβ42 or NTE-Aβ42 catalyze aggregation of all monomers. NTE-Aβ42 monomers display reduced aggregation rate with all kinds of seeds implying that extended termini interfere with the ability of monomers to nucleate or elongate. Cross-seeding or coaggregation may therefore represent an important contribution in the in vivo formation of assemblies believed to be important in disease.

Link to publication Citation for published version (APA): Bille, A., Linse, B., Mohanty, S., & Irbäck, A. (2015). Equilibrium simulation of trp-cage in the presence of protein crowders. Journal of Chemical Physics, 143(17), [175102]. DOI: 10.1063/1.4934997General rights Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights.• Users may download and print one copy of any publication from the public portal for the purpose of private study or research.• You may not further distribute the material or use it for any profit-making activity or commercial gain • You may freely distribute the URL identifying the publication in the public portal Take down policy If you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim. 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 replicaexchange 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. C 2015 AIP Publishing LLC. Equilibrium simulation of trp-cage in the presence of protein crowders[http://dx

Severe conditions and lack of cure for many amyloid diseases make it highly desired to understand the underlying principles of formation of fibrillar aggregates (amyloid). Here, amyloid formation from peptides was studied using Monte Carlo simulations. Systems of 20, 50, 100, 200 or 500 hexapeptides were simulated. Association kinetics were modeled equal for fibrillar and other (inter- and intra-peptide) contacts and assumed to be faster the lower the effective contact order, which represents the distance in space. Attempts to form contacts were thus accepted with higher probability the lower the effective contact order, whereby formation of new contacts next to preexisting ones is favored by shorter physical separation. Kinetic discrimination was invoked by using two different life-times for formed contacts. Contacts within amyloid fibrils were assumed to have on average longer life-time than other contacts. We find that the model produces fibrillation kinetics with a distinct lag phase, and that the fibrillar contacts need to dissociate on average 5-20 times slower than all other contacts for the fibrillar structure to dominate at equilibrium. Analysis of the species distribution along the aggregation process shows that no other intermediate is ever more populated than the dimer. Instead of a single nucleation event there is a concomitant increase in average aggregate size over the whole system, and the occurrence of multiple parallel processes makes the process more reproducible the larger the simulated system. The sigmoidal shape of the aggregation curves arises from cooperativity among multiple interactions within each pair of peptides in a fibril. A governing factor is the increasing probability as the aggregation process proceeds of neighboring reinforcing contacts. The results explain the very strong bias towards cross β-sheet fibrils in which the possibilities for cooperativity among interactions involving neighboring residues and the repetitive use of optimal side-chain interactions are explored at maximum.

Numerical properties of the smooth particle mesh Ewald (SPME) sum [U. Essmann, L. Perera, M. L. Berkowitz, T. Darden, H. Lee, and L. G. Pedersen, J. Chem. Phys. 103, 8577 (1995)] have been investigated by molecular dynamics simulation of ionic solutions and dipolar fluids. Scaling dependence of execution time on the number of particles at optimal performance have been determined and compared with the corresponding data of the standard Ewald (SE) sum. For both types of systems and over the range from N = 10(3) to 10(5) particles, the SPME sum displays a sub O(N ln N) complexity, whereas the SE sum possesses an O(N(3/2)) complexity. The breakeven of the simulation times appears at O(10(3)) particles, and the SPME sum is ≈20 times faster than the SE sum at 10(5) particles. Furthermore, energy truncation error and the energy and force execution time of the reciprocal space evaluation as function of the number of particles and the convergence parameters of the SPME sum have been determined for both types of systems containing up to 10(6) particles.

Proteins fold on a micros-ms time scale. However, the number of possible conformations of the polypeptide backbone is so large that random sampling would not allow the protein to fold within the lifetime of the universe, the Levinthal paradox. We show here that a protein chain can fold efficiently with high fidelity if on average native contacts survive longer than non-native ones, that is, if the dissociation rate constant for breakage of a contact is lower for native than for non-native interactions. An important consequence of this finding is that no pathway needs to be specified for a protein to fold. Instead, kinetic discrimination among formed contacts is a sufficient criterion for folding to proceed to the native state. Successful protein folding requires that productive contacts survive long enough to obtain a certain level of probability that other native contacts form before the first interacting unit dissociates. If native contacts survive longer than non-native ones, this prevents misfolding and provides the folding process with directionality toward the native state. If on average all contacts survive equally long, the protein chain is deemed to fold through random search through all possible conformations (i.e., the Levinthal paradox). A modest degree of cooperativity among the native contacts, that is, decreased dissociation rate next to neighboring contacts, shifts the required ratio of dissociation rates into a realistic regime and makes folding a stochastic process with a nucleation step. No kinetic discrimination needs to be invoked in regards to the association process, which is modeled as dependent on the diffusion rate of chain segments.

Dealing with missing data in data analysis is inevitable. Although powerful imputation methods that address this problem exist, there is still much room for improvement. In this study, we examined single imputation based on deep autoencoders, motivated by the apparent success of deep learning to efficiently extract useful dataset features. We have developed a consistent framework for both training and imputation. Moreover, we benchmarked the results against state-of-the-art imputation methods on different data sizes and characteristics. The work was not limited to the one-type variable dataset; we also imputed missing data with multi-type variables, e.g., a combination of binary, categorical, and continuous attributes. To evaluate the imputation methods, we randomly corrupted the complete data, with varying degrees of corruption, and then compared the imputed and original values. In all experiments, the developed autoencoder obtained the smallest error for all ranges of initial data corruption.

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