144 research outputs found
Correlations in the Sine-Gordon Model with Finite Soliton Density
We study the sine-Gordon (SG) model at finite densities of the topological
charge and small SG interaction constant, related to the one-dimensional
Hubbard model near half-filling. Using the modified WKB approach, we find that
the spectrum of the Gaussian fluctuations around the classical solution
reproduces the results of the Bethe ansatz studies. The modification of the
collective coordinate method allows us to write down the action, free from
infra-red divergencies. The behaviour of the density-type correlation functions
is non-trivial and we demonstrate the existence of leading and sub-leading
asymptotes. A consistent definition of the charge-raising operator is
discussed. The superconducting-type correlations are shown to decrease slowly
at small soliton densities, while the spectral weight of right (left) moving
fermions is spread over neighboring "4k_F" harmonics.Comment: 12 pages, 3 eps figures, REVTEX; a discussion of fermions is adde
A Bethe lattice representation for sandpiles
Avalanches in sandpiles are represented throughout a process of percolation
in a Bethe lattice with a feedback mechanism. The results indicate that the
frequency spectrum and probability distribution of avalanches resemble more to
experimental results than other models using cellular automata simulations.
Apparent discrepancies between experiments are reconciled. Critical behavior is
here expressed troughout the critical properties of percolation phenomena.Comment: 5 pages, 4 figures, submitted for publicatio
Fluctuations and correlations in sandpile models
We perform numerical simulations of the sandpile model for non-vanishing
driving fields and dissipation rates . Unlike simulations
performed in the slow driving limit, the unique time scale present in our
system allows us to measure unambiguously response and correlation functions.
We discuss the dynamic scaling of the model and show that
fluctuation-dissipation relations are not obeyed in this system.Comment: 5 pages, latex, 4 postscript figure
Discrete molecular dynamics simulations of peptide aggregation
We study the aggregation of peptides using the discrete molecular dynamics
simulations. At temperatures above the alpha-helix melting temperature of a
single peptide, the model peptides aggregate into a multi-layer parallel
beta-sheet structure. This structure has an inter-strand distance of 0.48 nm
and an inter-sheet distance of 1.0 nm, which agree with experimental
observations. In this model, the hydrogen bond interactions give rise to the
inter-strand spacing in beta-sheets, while the Go interactions among side
chains make beta-strands parallel to each other and allow beta-sheets to pack
into layers. The aggregates also contain free edges which may allow for further
aggregation of model peptides to form elongated fibrils.Comment: 15 pages, 8 figure
Tilt order parameters, polarity and inversion phenomena in smectic liquid crystals
The order parameters for the phenomenological description of the smectic-{\it
A} to smectic-{\it C} phase transition are formulated on the basis of molecular
symmetry and structure. It is shown that, unless the long molecular axis is an
axis of two-fold or higher rotational symmetry, the ordering of the molecules
in the smectic-{\it C} phase gives rise to more than one tilt order parameter
and to one or more polar order parameters. The latter describe the indigenous
polarity of the smectic-{\it C} phase, which is not related to molecular
chirality but underlies the appearance of spontaneous polarisation in chiral
smectics. A phenomenological theory of the phase transition is formulated by
means of a Landau expansion in two tilt order parameters (primary and
secondary) and an indigenous polarity order parameter. The coupling among these
order parameters determines the possibility of sign inversions in the
temperature dependence of the spontaneous polarisation and of the helical pitch
observed experimentally for some chiral smectic-{\it } materials. The
molecular interpretation of the inversion phenomena is examined in the light of
the new formulation.Comment: 12 pages, 5 figures, RevTe
Dimer Formation Enhances Structural Differences between Amyloid β-Protein (1–40) and (1–42): An Explicit-Solvent Molecular Dynamics Study
Amyloid -protein (A) is central to the pathology of Alzheimer's disease. A 5% difference in the primary structure of the two predominant alloforms, A and A, results in distinct assembly pathways and toxicity properties. Discrete molecular dynamics (DMD) studies of A and A assembly resulted in alloform-specific oligomer size distributions consistent with experimental findings. Here, a large ensemble of DMD–derived A and A monomers and dimers was subjected to fully atomistic molecular dynamics (MD) simulations using the OPLS-AA force field combined with two water models, SPCE and TIP3P. The resulting all-atom conformations were slightly larger, less compact, had similar turn and lower -strand propensities than those predicted by DMD. Fully atomistic A and A monomers populated qualitatively similar free energy landscapes. In contrast, the free energy landscape of A dimers indicated a larger conformational variability in comparison to that of A dimers. A dimers were characterized by an increased flexibility in the N-terminal region D1-R5 and a larger solvent exposure of charged amino acids relative to A dimers. Of the three positively charged amino acids, R5 was the most and K16 the least involved in salt bridge formation. This result was independent of the water model, alloform, and assembly state. Overall, salt bridge propensities increased upon dimer formation. An exception was the salt bridge propensity of K28, which decreased upon formation of A dimers and was significantly lower than in A dimers. The potential relevance of the three positively charged amino acids in mediating the A oligomer toxicity is discussed in the light of available experimental data
A Condensation-Ordering Mechanism in Nanoparticle-Catalyzed Peptide Aggregation
Nanoparticles introduced in living cells are capable of strongly promoting
the aggregation of peptides and proteins. We use here molecular dynamics
simulations to characterise in detail the process by which nanoparticle
surfaces catalyse the self- assembly of peptides into fibrillar structures. The
simulation of a system of hundreds of peptides over the millisecond timescale
enables us to show that the mechanism of aggregation involves a first phase in
which small structurally disordered oligomers assemble onto the nanoparticle
and a second phase in which they evolve into highly ordered beta-sheets as
their size increases
Conformational Preferences of a 14-Residue Fibrillogenic Peptide from Acetylcholinesteraseâ€
A 14-residue fragment from near the C-terminus of the enzyme acetylcholinesterase (AChE) is believed to have a neurotoxic/neurotrophic effect acting via an unknown pathway. While the peptide is α-helical in the full-length enzyme, the structure and association mechanism of the fragment are unknown. Using multiple molecular dynamics simulations, starting from a tetrameric complex of the association domain of AChE and systematicall disassembled subsets that include the peptide fragment, we show that the fragment is incapable of retaining its helicity in solution. Extensive replica exchange Monte Carlo folding and unfolding simulations in implicit solvent with capped and uncappted termini failed to converge to any consistent cluster of structures, suggesting that the fragment remains largely unstructured in solution under the conditions considered. Furthermore, extended molecular dynamics simulations of two steric zipper models show that the peptide is likely to form a zipper with antiparallel sheets and that peptides with mutations known to prevent fibril formation likely do so by interfering with this packing. The results demonstrate how the local environment of a peptide can stabilize a particular conformation
Impact of Single Links in Competitive Percolation -- How complex networks grow under competition
How a complex network is connected crucially impacts its dynamics and
function. Percolation, the transition to extensive connectedness upon gradual
addition of links, was long believed to be continuous but recent numerical
evidence on "explosive percolation" suggests that it might as well be
discontinuous if links compete for addition. Here we analyze the microscopic
mechanisms underlying discontinuous percolation processes and reveal a strong
impact of single link additions. We show that in generic competitive
percolation processes, including those displaying explosive percolation, single
links do not induce a discontinuous gap in the largest cluster size in the
thermodynamic limit. Nevertheless, our results highlight that for large finite
systems single links may still induce observable gaps because gap sizes scale
weakly algebraically with system size. Several essentially macroscopic clusters
coexist immediately before the transition, thus announcing discontinuous
percolation. These results explain how single links may drastically change
macroscopic connectivity in networks where links add competitively.Comment: non-final version, for final see Nature Physics homepag
In Silico Analysis of the Apolipoprotein E and the Amyloid β Peptide Interaction: Misfolding Induced by Frustration of the Salt Bridge Network
The relationship between Apolipoprotein E (ApoE) and the aggregation processes of the amyloid β (Aβ) peptide has been shown to be crucial for Alzheimer's disease (AD). The presence of the ApoE4 isoform is considered to be a contributing risk factor for AD. However, the detailed molecular properties of ApoE4 interacting with the Aβ peptide are unknown, although various mechanisms have been proposed to explain the physiological and pathological role of this relationship. Here, computer simulations have been used to investigate the process of Aβ interaction with the N-terminal domain of the human ApoE isoforms (ApoE2, ApoE3 and ApoE4). Molecular docking combined with molecular dynamics simulations have been undertaken to determine the Aβ peptide binding sites and the relative stability of binding to each of the ApoE isoforms. Our results show that from the several ApoE isoforms investigated, only ApoE4 presents a misfolded intermediate when bound to Aβ. Moreover, the initial α-helix used as the Aβ peptide model structure also becomes unstructured due to the interaction with ApoE4. These structural changes appear to be related to a rearrangement of the salt bridge network in ApoE4, for which we propose a model. It seems plausible that ApoE4 in its partially unfolded state is incapable of performing the clearance of Aβ, thereby promoting amyloid forming processes. Hence, the proposed model can be used to identify potential drug binding sites in the ApoE4-Aβ complex, where the interaction between the two molecules can be inhibited
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