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

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

Generic Mechanism of Emergence of Amyloid Protofilaments from Disordered Oligomeric aggregates

The presence of oligomeric aggregates, which is often observed during the process of amyloid formation, has recently attracted much attention since it has been associated with neurodegenerative conditions such as Alzheimer's and Parkinson's diseases. We provide a description of a sequence-indepedent mechanism by which polypeptide chains aggregate by forming metastable oligomeric intermediate states prior to converting into fibrillar structures. Our results illustrate how the formation of ordered arrays of hydrogen bonds drives the formation of beta-sheets within the disordered oligomeric aggregates that form early under the effect of hydrophobic forces. Initially individual beta-sheets form with random orientations, which subsequently tend to align into protofilaments as their lengths increases. Our results suggest that amyloid aggregation represents an example of the Ostwald step rule of first order phase transitions by showing that ordered cross-beta structures emerge preferentially from disordered compact dynamical intermediate assemblies.Comment: 14 pages, 4 figure

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

Fluctuations and correlations in sandpile models

We perform numerical simulations of the sandpile model for non-vanishing driving fields $h$ and dissipation rates $\epsilon$. 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

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 $C^{\ast}$} materials. The molecular interpretation of the inversion phenomena is examined in the light of the new formulation.Comment: 12 pages, 5 figures, RevTe

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

Automated identification of neurons and their locations

Individual locations of many neuronal cell bodies (>10^4) are needed to enable statistically significant measurements of spatial organization within the brain such as nearest-neighbor and microcolumnarity measurements. In this paper, we introduce an Automated Neuron Recognition Algorithm (ANRA) which obtains the (x,y) location of individual neurons within digitized images of Nissl-stained, 30 micron thick, frozen sections of the cerebral cortex of the Rhesus monkey. Identification of neurons within such Nissl-stained sections is inherently difficult due to the variability in neuron staining, the overlap of neurons, the presence of partial or damaged neurons at tissue surfaces, and the presence of non-neuron objects, such as glial cells, blood vessels, and random artifacts. To overcome these challenges and identify neurons, ANRA applies a combination of image segmentation and machine learning. The steps involve active contour segmentation to find outlines of potential neuron cell bodies followed by artificial neural network training using the segmentation properties (size, optical density, gyration, etc.) to distinguish between neuron and non-neuron segmentations. ANRA positively identifies 86[5]% neurons with 15[8]% error (mean[st.dev.]) on a wide range of Nissl-stained images, whereas semi-automatic methods obtain 80[7]%/17[12]%. A further advantage of ANRA is that it affords an unlimited increase in speed from semi-automatic methods, and is computationally efficient, with the ability to recognize ~100 neurons per minute using a standard personal computer. ANRA is amenable to analysis of huge photo-montages of Nissl-stained tissue, thereby opening the door to fast, efficient and quantitative analysis of vast stores of archival material that exist in laboratories and research collections around the world.Comment: 38 pages. Formatted for two-sided printing. Supplemental material and software available at http://physics.bu.edu/~ainglis/ANRA

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

Discrete molecular dynamics simulations of peptide aggregation

We study the aggregation of peptides using the discrete molecular dynamics simulations. Specifically, at temperatures above the alpha-helix melting temperature of a single peptide, the model peptides aggregate into a multilayer parallel beta-sheet structure. This structure has an interstrand distance of 4.8 A and an intersheet distance of 10 A, which agree with experimental observations. Our model explains these results as follows: hydrogen-bond interactions give rise to the interstrand spacing in beta sheets, while Gō interactions between side chains make beta strands parallel to each other and allow beta sheets to pack into layers. An important feature of our results is that the aggregates contain free edges, which may allow for further aggregation of model peptides to form elongated fibrils