Statistical Mechanical Treatments of Protein Amyloid Formation

Protein aggregation is an important field of investigation because it is closely related to the problem of neurodegenerative diseases, to the development of biomaterials, and to the growth of cellular structures such as cyto-skeleton. Self-aggregation of protein amyloids, for example, is a complicated process involving many species and levels of structures. This complexity, however, can be dealt with using statistical mechanical tools, such as free energies, partition functions, and transfer matrices. In this article, we review general strategies for studying protein aggregation using statistical mechanical approaches and show that canonical and grand canonical ensembles can be used in such approaches. The grand canonical approach is particularly convenient since competing pathways of assembly and dis-assembly can be considered simultaneously. Another advantage of using statistical mechanics is that numerically exact solutions can be obtained for all of the thermodynamic properties of fibrils, such as the amount of fibrils formed, as a function of initial protein concentration. Furthermore, statistical mechanics models can be used to fit experimental data when they are available for comparison.Comment: Accepted to IJM

A Statistical Mechanical Approach to Protein Aggregation

We develop a theory of aggregation using statistical mechanical methods. An example of a complicated aggregation system with several levels of structures is peptide/protein self-assembly. The problem of protein aggregation is important for the understanding and treatment of neurodegenerative diseases and also for the development of bio-macromolecules as new materials. We write the effective Hamiltonian in terms of interaction energies between protein monomers, protein and solvent, as well as between protein filaments. The grand partition function can be expressed in terms of a Zimm-Bragg-like transfer matrix, which is calculated exactly and all thermodynamic properties can be obtained. We start with two-state and three-state descriptions of protein monomers using Potts models that can be generalized to include q-states, for which the exactly solvable feature of the model remains. We focus on n X N lattice systems, corresponding to the ordered structures observed in some real fibrils. We have obtained results on nucleation processes and phase diagrams, in which a protein property such as the sheet content of aggregates is expressed as a function of the number of proteins on the lattice and inter-protein or interfacial interaction energies. We have applied our methods to A{\beta}(1-40) and Curli fibrils and obtained results in good agreement with experiments.Comment: 13 pages, 8 figures, accepted to J. Chem. Phy

Exactly Solvable Model for Helix-Coil-Sheet Transitions in Protein Systems

In view of the important role helix-sheet transitions play in protein aggregation, we introduce a simple model to study secondary structural transitions of helix-coil-sheet systems using a Potts model starting with an effective Hamiltonian. This energy function depends on four parameters that approximately describe entropic and enthalpic contributions to the stability of a polypeptide in helical and sheet conformations. The sheet structures involve long-range interactions between residues which are far in sequence, but are in contact in real space. Such contacts are included in the Hamiltonian. Using standard statistical mechanical techniques, the partition function is solved exactly using transfer matrices. Based on this model, we study thermodynamic properties of polypeptides, including phase transitions between helix, sheet, and coil structures.Comment: Updated version with correction

Self-assembly of two-dimensional binary quasicrystals: A possible route to a DNA quasicrystal

We use Monte Carlo simulations and free-energy techniques to show that binary solutions of penta- and hexavalent two-dimensional patchy particles can form thermodynamically stable quasicrystals even at very narrow patch widths, provided their patch interactions are chosen in an appropriate way. Such patchy particles can be thought of as a coarse-grained representation of DNA multi-arm `star' motifs, which can be chosen to bond with one another very specifically by tuning the DNA sequences of the protruding arms. We explore several possible design strategies and conclude that DNA star tiles that are designed to interact with one another in a specific but not overly constrained way could potentially be used to construct soft quasicrystals in experiment. We verify that such star tiles can form stable dodecagonal motifs using oxDNA, a realistic coarse-grained model of DNA

Stochastic Kinetic Study of Protein Aggregation and Molecular Crowding Effects of Ab40 and Ab42

Two isoforms of beta amyloid peptides, Ab40 and Ab42, differ from each other only in the last two amino acids, IA, at the end of Ab42. They, however, differ significantly in their ability in inducing Alzheimer's disease (AD). The rate curves of fibril growth of Ab40 and Ab42 and the effects of molecular crowding have been measured in in vitro experiments. These experimental curves, on the other hand, have been fitted in terms of rate constants for elementary reaction steps using rate equation approaches. Several sets of such rate parameters have been reported in the literature. Employing a recently developed stochastic kinetic method, implemented in a browser-based simulator, popsim, we study to reveal the differences in the kinetic behaviors implied by these sets of rate parameters. In particular, the stochastic method is used to distinguish the kinetic behaviors between Ab40 and Ab42 isoforms. As a result, we make general comments on the usefulness of these sets of rate parameters.Comment: To appear in the Journal of the Chinese Chemical Societ

Mimicking non-ideal instrument behavior for hologram processing using neural style translation

Holographic cloud probes provide unprecedented information on cloud particle density, size and position. Each laser shot captures particles within a large volume, where images can be computationally refocused to determine particle size and shape. However, processing these holograms, either with standard methods or with machine learning (ML) models, requires considerable computational resources, time and occasional human intervention. ML models are trained on simulated holograms obtained from the physical model of the probe since real holograms have no absolute truth labels. Using another processing method to produce labels would be subject to errors that the ML model would subsequently inherit. Models perform well on real holograms only when image corruption is performed on the simulated images during training, thereby mimicking non-ideal conditions in the actual probe (Schreck et. al, 2022). Optimizing image corruption requires a cumbersome manual labeling effort. Here we demonstrate the application of the neural style translation approach (Gatys et. al, 2016) to the simulated holograms. With a pre-trained convolutional neural network (VGG-19), the simulated holograms are ``stylized'' to resemble the real ones obtained from the probe, while at the same time preserving the simulated image ``content'' (e.g. the particle locations and sizes). Two image similarity metrics concur that the stylized images are more like real holograms than the synthetic ones. With an ML model trained to predict particle locations and shapes on the stylized data sets, we observed comparable performance on both simulated and real holograms, obviating the need to perform manual labeling. The described approach is not specific to hologram images and could be applied in other domains for capturing noise and imperfections in observational instruments to make simulated data more like real world observations.Comment: 23 pages, 9 figure