110 research outputs found
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
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