379 research outputs found
Phase Diagram of alpha-Helical and beta-Sheet Forming Peptides
The intrinsic property of proteins to form structural motifs such as
alpha-helices and beta-sheets leads to a complex phase behavior in which
proteins can assemble into various types of aggregates including crystals,
liquidlike phases of unfolded or natively folded proteins, and amyloid fibrils.
Here we use a coarse-grained protein model that enables us to perform Monte
Carlo simulations for determining the phase diagram of natively folded
alpha-helical and unfolded beta-sheet forming peptides. The simulations reveal
the existence of various metastable peptide phases. The liquidlike phases are
metastable with respect to the fibrillar phases, and there is a hierarchy of
metastability
Nucleation of amyloid fibrils
We consider nucleation of amyloid fibrils in the case when the process occurs
by the mechanism of direct polymerization of practically fully extended protein
segments, i.e. beta-strands, into beta-sheets. Applying the classical
nucleation theory, we derive a general expression for the work to form a
nanosized amyloid fibril (protofilament) constituted of successively layered
beta-sheets. Analysis of this expression reveals that with increasing its size,
the fibril transforms from one-dimensional into two-dimensional aggregate in
order to preserve the equilibrium shape corresponding to minimal formation
work. We determine the size of the fibril nucleus, the fibril nucleation work
and the fibril nucleation rate as explicit functions of the concentration and
temperature of the protein solution. The results obtained are applicable to
homogeneous nucleation which occurs when the solution is sufficiently pure
and/or strongly supersaturated
Nucleation of colloids and macromolecules: does the nucleation pathway matter?
A recent description of diffusion-limited nucleation based on fluctuating
hydrodynamics that extends classical nucleation theory predicts a very
non-classical two-step scenario whereby nucleation is most likely to occur in
spatially-extended, low-amplitude density fluctuations. In this paper, it is
shown how the formalism can be used to determine the maximum probability of
observing \emph{any} proposed nucleation pathway, thus allowing one to address
the question as to their relative likelihood, including of the newly proposed
pathway compared to classical scenarios. Calculations are presented for the
nucleation of high-concentration bubbles in a low-concentration solution of
globular proteins and it is found that the relative probabilities (new theory
compared to classical result) for reaching a critical nucleus containing
molecules scales as thus indicating that for all but the smallest
nuclei, the classical scenario is extremely unlikely.Comment: 7 pages, 5 figure
Stochastic self-assembly of incommensurate clusters
We examine the classic problem of homogeneous nucleation and growth by
deriving and analyzing a fully discrete stochastic master equation. Upon
comparison with results obtained from the corresponding mean-field
Becker-D\"{o}ring equations we find striking differences between the two
corresponding equilibrium mean cluster concentrations. These discrepancies
depend primarily on the divisibility of the total available mass by the maximum
allowed cluster size, and the remainder. When such mass incommensurability
arises, a single remainder particle can "emulsify" or "disperse" the system by
significantly broadening the mean cluster size distribution. This finite-sized
broadening effect is periodic in the total mass of the system and can arise
even when the system size is asymptotically large, provided the ratio of the
total mass to the maximum cluster size is finite. For such finite ratios we
show that homogeneous nucleation in the limit of large, closed systems is not
accurately described by classical mean-field mass-action approaches.Comment: 5 pages, 4 figures, 1 tabl
Nucleation in scale-free networks
We have studied nucleation dynamics of the Ising model in scale-free networks
with degree distribution by using forward flux sampling
method, focusing on how the network topology would influence the nucleation
rate and pathway. For homogeneous nucleation, the new phase clusters grow from
those nodes with smaller degree, while the cluster sizes follow a power-law
distribution. Interestingly, we find that the nucleation rate decays
exponentially with the network size , and accordingly the critical nucleus
size increases linearly with , implying that homogeneous nucleation is not
relevant in the thermodynamic limit. These observations are robust to the
change of and also present in random networks. In addition, we have
also studied the dynamics of heterogeneous nucleation, wherein impurities
are initially added, either to randomly selected nodes or to targeted ones with
largest degrees. We find that targeted impurities can enhance the nucleation
rate much more sharply than random ones. Moreover, scales as and for targeted and
random impurities, respectively. A simple mean field analysis is also present
to qualitatively illustrate above simulation results.Comment: 7 pages, 5 figure
Heterogeneous condensation of the Lennard-Jones vapor onto a nanoscale seed particle
The heterogeneous condensation of a Lennard-Jones vapor onto a nanoscale seed
particle is studied using molecular dynamics simulations. Measuring the
nucleation rate and the height of the free energy barrier using the mean first
passage time method shows that the presence of a weakly interacting seed has
little effect on the work of forming very small cluster embryos but accelerates
the rate by lowering the barrier for larger clusters. We suggest that this
results from a competition between the energetic and entropic features of
cluster formation in the bulk and at the heterogeneity. As the interaction is
increased, the free energy of formation is reduced for all cluster sizes. We
also develop a simple phenomenological model of film formation on a small seed
that captures the general features of the nucleation process for small
heterogeneities. A comparison of our simulation results with the model shows
that heterogeneous classical nucleation theory provides a good estimate of the
critical size of the film but significantly over-estimates the size of the
barrier.Comment: 9 pages, 10 figures, In Print J. Chem. Phy
Crystal nucleation and cluster-growth kinetics in a model glass under shear
Crystal nucleation and growth processes induced by an externally applied
shear strain in a model metallic glass are studied by means of nonequilibrium
molecular dynamics simulations, in a range of temperatures. We observe that the
nucleation-growth process takes place after a transient, induction regime. The
critical cluster size and the lag-time associated with this induction period
are determined from a mean first-passage time analysis. The laws that describe
the cluster growth process are studied as a function of temperature and strain
rate. A theoretical model for crystallization kinetics that includes the time
dependence for nucleation and cluster growth is developed within the framework
of the Kolmogorov-Johnson-Mehl-Avrami scenario and is compared with the
molecular dynamics data. Scalings for the cluster growth laws and for the
crystallization kinetics are also proposed and tested. The observed nucleation
rates are found to display a nonmonotonic strain rate dependency
A dynamical theory of homogeneous nucleation for colloids and macromolecules
Homogeneous nucleation is formulated within the context of fluctuating
hydrodynamics. It is shown that for a colloidal or macromolecular system in the
strong damping limit the most likely path for nucleation can be determined by
gradient descent in density space governed by a nontrivial metric fixed by the
dynamics. The theory provides a justification and extension of more heuristic
equilibrium approaches based solely on the free energy. It is illustrated by
application to liquid-vapor nucleation where it is shown that, in contrast to
most free energy-based studies, the smallest clusters correspond to long
wavelength, small amplitude perturbations.Comment: final version; 4 pages, 2 figure
Systematically extending classical nucleation theory
The foundation for any discussion of first-order phse transitions is
Classical Nucleation Theory(CNT). CNT, developed in the first half of the
twentieth century, is based on a number of heuristically plausible assumtptions
and the majority of theoretical work on nucleation is devoted to refining or
extending these ideas. Ideally, one would like to derive CNT from a more
fundamental description of nucleation so that its extension, development and
refinement could be developed systematically. In this paper, such a development
is described based on a previously established (Lutsko, JCP 136:034509, 2012 )
connection between Classical Nucleation Theory and fluctuating hydrodynamics.
Here, this connection is described without the need for artificial assumtions
such as spherical symmetry. The results are illustrated by application to CNT
with moving clusters (a long-standing problem in the literature) and the
constructrion of CNT for ellipsoidal clusters
Approaching equilibrium and the distribution of clusters
We investigate the approach to stable and metastable equilibrium in Ising
models using a cluster representation. The distribution of nucleation times is
determined using the Metropolis algorithm and the corresponding
model using Langevin dynamics. We find that the nucleation rate is suppressed
at early times even after global variables such as the magnetization and energy
have apparently reached their time independent values. The mean number of
clusters whose size is comparable to the size of the nucleating droplet becomes
time independent at about the same time that the nucleation rate reaches its
constant value. We also find subtle structural differences between the
nucleating droplets formed before and after apparent metastable equilibrium has
been established.Comment: 22 pages, 16 figure
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