4,434 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
Quantum coherence of the molecular states and their corresponding currents in nanoscale Aharonov-Bohm interferometers
By considering a nanoscale Aharonov-Bohm (AB) interferometer containing a
parrallel-coupled double dot coupled to the source and drain electrodes, we
investigate the AB phase oscillations of transport current via the bonding and
antibonding state channels. The results we obtained justify the experimental
analysis given in [Phys. Rev. Lett. \textbf{106}, 076801 (2011)] that bonding
state currents in different energy configurations are almost the same. On the
other hand, we extend the analysis to the transient transport current
components flowing through different channels, to explore the effect of the
parity of bonding and antibonding states on the AB phase dependence of the
corresponding current components in the transient regime. The relations of the
AB phase dependence between the quantum states and the associated current
components are analyzed in details, which provides useful information for the
reconstruction of quantum states through the measurement of the transport
current in such systems. With the coherent properties in the quantum dot states
as well as in the transport currents, we also provide a way to manipulate the
bonding and antibonding states by the AB magnetic flux.Comment: 10 pages, 7 figure
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