Description of microcolumnar ensembles in association cortex and their disruption in Alzheimer and Lewy body dementias

The cortex of the brain is organized into clear horizontal layers, laminae, which subserve much of the connectional anatomy of the brain. We hypothesize that there is also a vertical anatomical organization that might subserve local interactions of neuronal functional units, in accord with longstanding electrophysiological observations. We develop and apply a general quantitative method, inspired by analogous methods in condensed matter physics, to examine the anatomical organization of the cortex in human brain. We find, in addition to obvious laminae, anatomical evidence for tightly packed microcolumnar ensembles containing approximately 11 neurons, with a periodicity of about 80 microm. We examine the structural integrity of this new architectural feature in two common dementing illnesses, Alzheimer disease and dementia with Lewy bodies. In Alzheimer disease, there is a dramatic, nearly complete loss of microcolumnar ensemble organization. The relative degree of loss of microcolumnar ensembles is directly proportional to the number of neurofibrillary tangles, but not related to the amount of amyloid-beta deposition. In dementia with Lewy bodies, a similar disruption of microcolumnar ensemble architecture occurs despite minimal neuronal loss. These observations show that quantitative analysis of complex cortical architecture can be applied to analyze the anatomical basis of brain disorders.

Species independence of mutual information in coding and noncoding DNA

We explore if there exist universal statistical patterns that are different in coding and noncoding DNA and can be found in all living organisms, regardless of their phylogenetic origin. We find that (i) the mutual information function [symbol: see text] has a significantly different functional form in coding and noncoding DNA. We further find that (ii) the probability distributions of the average mutual information [symbol: see text] are significantly different in coding and noncoding DNA, while (iii) they are almost the same for organisms of all taxonomic classes. Surprisingly, we find that [symbol: see text] is capable of predicting coding regions as accurately as organism-specific coding measures.

Multifractal properties of the random resistor network

We study the multifractal spectrum of the current in the two-dimensional random resistor network at the percolation threshold. We consider two ways of applying the voltage difference: (i) two parallel bars, and (ii) two points. Our numerical results suggest that in the infinite system limit, the probability distribution behaves for small i as P(i) approximately 1/i, where i is the current. As a consequence, the moments of i of order q</=q(c)=0 do not exist and all currents of value below the most probable one have the fractal dimension of the backbone. The backbone can thus be described in terms of only (i) blobs of fractal dimension d(B) and (ii) high current carrying bonds of fractal dimension going from 1/nu to d(B).

Identifying the protein folding nucleus using molecular dynamics

Molecular dynamics simulations of folding in an off-lattice protein model reveal a nucleation scenario, in which a few well-defined contacts are formed with high probability in the transition state ensemble of conformations. Their appearance determines folding cooperativity and drives the model protein into its folded conformation. Amino acid residues participating in those contacts may serve as "accelerator pedals" used by molecular evolution to control protein folding rate.

Distributions of dimeric tandem repeats in non-coding and coding DNA sequences

We study the length distribution functions for the 16 possible distinct dimeric tandem repeats in DNA sequences of diverse taxonomic partitions of GenBank (known human and mouse genomes, and complete genomes of Caenorhabditis elegans and yeast). For coding DNA, we find that all 16 distribution functions are exponential. For non-coding DNA, the distribution functions for most of the dimeric repeats have surprisingly long tails, that fit a power-law function. We hypothesize that: (i) the exponential distributions of dimeric repeats in protein coding sequences indicate strong evolutionary pressure against tandem repeat expansion in coding DNA sequences; and (ii) long tails in the distributions of dimers in non-coding DNA may be a result of various mutational mechanisms. These long, non-exponential tails in the distribution of dimeric repeats in non-coding DNA are hypothesized to be due to the higher tolerance of non-coding DNA to mutations. By comparing genomes of various phylogenetic types of organisms, we find that the shapes of the distributions are not universal, but rather depend on the specific class of species and the type of a dimer.

Decomposition of heartbeat time series: scaling analysis of the sign sequence

The cardiac interbeat (RR) increment time series can be decomposed into two sub-sequences: a magnitude series and a sign series. The authors show that the sign sequence, a simple binary representation of the original RR series, retains fundamental scaling properties of the original series, is robust with respect to outliers, and may provide useful information about neuroautonomic control mechanisms.

Application of statistical physics to heartbeat diagnosis

We present several recent studies based on statistical physics concepts that can be used as diagnostic tools for heart failure. We describe the scaling exponent characterizing the long-range correlations in heartbeat time series as well as the multifractal features recently discovered in heartbeat rhythm. It is found that both features, the long-range correlations and the multifractility, are weaker in cases of heart failure.

Sleep-wake differences in scaling behavior of the human heartbeat: analysis of terrestrial and long-term space flight data

We compare scaling properties of the cardiac dynamics during sleep and wake periods for healthy individuals, cosmonauts during orbital flight, and subjects with severe heart disease. For all three groups, we find a greater degree of anticorrelation in the heartbeat fluctuations during sleep compared to wake periods. The sleep-wake difference in the scaling exponents for the three groups is comparable to the difference between healthy and diseased individuals. The observed scaling differences are not accounted for simply by different levels of activity, but appear related to intrinsic changes in the neuroautonomic control of the heartbeat.

Waterlike anomalies for core-softened models of fluids: one dimension

We use a one-dimensional (1D) core-softened potential to develop a physical picture for some of the anomalies present in liquid water. The core-softened potential mimics the effect of hydrogen bonding. The interest in the 1D system stems from the facts that closed-form results are possible and that the qualitative behavior in 1D is reproduced in the liquid phase for higher dimensions. We discuss the relation between the shape of the potential and the density anomaly, and we study the entropy anomaly resulting from the density anomaly. We find that certain forms of the two-step square-well potential lead to the existence at T=0 of a low-density phase favored at low pressures and of a high-density phase favored at high pressures, and to the appearance of a point C' at a positive pressure, which is the analog of the T=0 "critical point" in the 1D Ising model. The existence of point C' leads to anomalous behavior of the isothermal compressibility K(T) and the isobaric specific heat C(P).

Scaling of the distribution of price fluctuations of individual companies

We present a phenomenological study of stock price fluctuations of individual companies. We systematically analyze two different databases covering securities from the three major U.S. stock markets: (a) the New York Stock Exchange, (b) the American Stock Exchange, and (c) the National Association of Securities Dealers Automated Quotation stock market. Specifically, we consider (i) the trades and quotes database, for which we analyze 40 million records for 1000 U.S. companies for the 2-yr period 1994-95; and (ii) the Center for Research and Security Prices database, for which we analyze 35 million daily records for approximately 16,000 companies in the 35-yr period 1962-96. We study the probability distribution of returns over varying time scales Delta t, where Delta t varies by a factor of approximately 10(5), from 5 min up to approximately 4 yr. For time scales from 5 min up to approximately 16 days, we find that the tails of the distributions can be well described by a power-law decay, characterized by an exponent 2.5 < proportional to < 4, well outside the stable Lévy regime 0 < alpha < 2. For time scales Delta t >> (Delta t)(x) approximately equal to 16 days, we observe results consistent with a slow convergence to Gaussian behavior. We also analyze the role of cross correlations between the returns of different companies and relate these correlations to the distribution of returns for market indices.

Dynamics of simulated water under pressure

We present molecular dynamics simulations of the extended simple-point-charge model of water to probe the dynamic properties at temperatures from 350 K down to 190 K and pressures from 2.5 GPa (25 kbar) down to -300 MPa (-3 kbar). We compare our results with those obtained experimentally, both of which show a diffusivity maximum as a function of pressure. We find that our simulation results are consistent with the predictions of the mode-coupling theory for the dynamics of weakly supercooled liquids--strongly supporting the hypothesis that the apparent divergences of dynamic properties observed experimentally may be independent of a possible thermodynamic singularity at low temperature. The dramatic change in water's dynamic and structural properties as a function of pressure allows us to confirm the predictions of MCT over a much broader range of the von Schweidler exponent values than has been studied for simple atomic liquids. We also show how structural changes are reflected in the wave-vector dependence of dynamic properties of the liquid along a path of nearly constant diffusivity. For temperatures below the crossover temperature of MCT (where the predictions of MCT are expected to fail), we find tentative evidence for a crossover of the temperature dependence of the diffusivity from power-law to Arrhenius behavior, with an activation energy typical of a strong liquid.

Scaling of the distribution of fluctuations of financial market indices

We study the distribution of fluctuations of the S&P 500 index over a time scale deltat by analyzing three distinct databases. Database (i) contains approximately 1 200 000 records, sampled at 1-min intervals, for the 13-year period 1984-1996, database (ii) contains 8686 daily records for the 35-year period 1962-1996, and database (iii) contains 852 monthly records for the 71-year period 1926-1996. We compute the probability distributions of returns over a time scale deltat, where deltat varies approximately over a factor of 10(4)-from 1 min up to more than one month. We find that the distributions for deltat<or= 4 d (1560 min) are consistent with a power-law asymptotic behavior, characterized by an exponent alpha approximately 3, well outside the stable Lévy regime 0<alpha<2. To test the robustness of the S&P result, we perform a parallel analysis on two other financial market indices. Database (iv) contains 3560 daily records of the NIKKEI index for the 14-year period 1984-1997, and database (v) contains 4649 daily records of the Hang-Seng index for the 18-year period 1980-1997. We find estimates of alpha consistent with those describing the distribution of S&P 500 daily returns. One possible reason for the scaling of these distributions is the long persistence of the autocorrelation function of the volatility. For time scales longer than (deltat)x approximately 4 d, our results are consistent with a slow convergence to Gaussian behavior.

Fluid flow through ramified structures

We investigate the fluid flow through two-dimensional ramified structures by direct simulation of the Navier-Stokes equations. We show that for trees with n generations, the flow distribution strongly depends on the Reynolds number Re. Specifically, for a tree without loops the flow becomes highly heterogeneous at high Re. For a tree with loops, on the other hand, the flow distribution tends to be more uniform at increased Re conditions. We show that these apparently contradictory behaviors have the same origin, namely, the effect of inertia on the momentum transport in the channels of the ramified geometry. In order to simulate the propagation of the flow imbalance throughout the tree without loops, we develop a simple model that incorporates the basic fluid dynamics features of the system. For large trees, the results of the model indicate that the distribution of flow at the outlet branches can be described by a self-affine landscape. Finally, we argue that the nonuniform partitioning of flow found for the structure without loops may contribute to the morphogenesis and functioning of the bronchial tree.

Scaling in nature: from DNA through heartbeats to weather

The purpose of this report is to describe some recent progress in applying scaling concepts to various systems in nature. We review several systems characterized by scaling laws such as DNA sequences, heartbeat rates and weather variations. We discuss the finding that the exponent alpha quantifying the scaling in DNA in smaller for coding than for noncoding sequences. We also discuss the application of fractal scaling analysis to the dynamics of heartbeat regulation, and report the recent finding that the scaling exponent alpha is smaller during sleep periods compared to wake periods. We also discuss the recent findings that suggest a universal scaling exponent characterizing the weather fluctuations.

Optimizing the success of random searches

We address the general question of what is the best statistical strategy to adapt in order to search efficiently for randomly located objects ('target sites'). It is often assumed in foraging theory that the flight lengths of a forager have a characteristic scale: from this assumption gaussian, Rayleigh and other classical distributions with well-defined variances have arisen. However, such theories cannot explain the long-tailed power-law distributions of flight lengths or flight times that are observed experimentally. Here we study how the search efficiency depends on the probability distribution of flight lengths taken by a forager that can detect target sites only in its limited vicinity. We show that, when the target sites are sparse and can be visited any number of times, an inverse square power-law distribution of flight lengths, corresponding to Lévy flight motion, is an optimal strategy. We test the theory by analysing experimental foraging data on selected insect, mammal and bird species, and find that they are consistent with the predicted inverse square power-law distributions.

Scaling behavior in crackle sound during lung inflation

During slow inflation of lung lobes, we measure a sequence of short explosive transient sound waves called "crackles," each consisting of an initial spike followed by ringing. The crackle time series is irregular and intermittent, with the number of spikes of size s following a power law, n(s) proportional, variants(-alpha), with alpha=2.77+/-0.05. We develop a model of crackle wave generation and propagation in a tree structure that combines the avalanchelike opening of airway segments with the wave propagation of crackles in a tree structure. The agreement between experiments and simulations suggests that (i) the irregularities are a consequence of structural heterogeneity in the lung, (ii) the intermittent behavior is due to the avalanchelike opening, and (iii) the scaling is a result of successive attenuations acting on the sound spikes as they propagate through a cascade of bifurcations along the airway tree.

Quasicrystals in a monodisperse system

We investigate the formation of a two-dimensional quasicrystal in a monodisperse system, using molecular dynamics simulations of hard-sphere particles interacting via a two-dimensional square-well potential. We find that more than one stable crystalline phase can form for certain values of the square-well parameters. Quenching the liquid phase at a very low temperature, we obtain an amorphous phase. By heating this amorphous phase, we obtain a quasicrystalline structure with fivefold symmetry. From estimations of the Helmholtz potentials of the stable crystalline phases and of the quasicrystal, we conclude that the observed quasicrystal phase can be the stable phase in a specific range of temperatures.

Traveling time and traveling length in critical percolation clusters

We study traveling time and traveling length for tracer dispersion in two-dimensional bond percolation, modeling flow by tracer particles driven by a pressure difference between two points separated by Euclidean distance r. We find that the minimal traveling time t(min) scales as t(min) approximately r(1.33), which is different from the scaling of the most probable traveling time, t* approximately r(1.64). We also calculate the length of the path corresponding to the minimal traveling time and find l(min) approximately r(1.13) and that the most probable traveling length scales as l* approximately r(1.21). We present the relevant distribution functions and scaling relations.

Statistical properties of the volatility of price fluctuations

We study the statistical properties of volatility, measured by locally averaging over a time window T, the absolute value of price changes over a short time interval deltat. We analyze the S&P 500 stock index for the 13-year period Jan. 1984 to Dec. 1996. We find that the cumulative distribution of the volatility is consistent with a power-law asymptotic behavior, characterized by an exponent mu approximately 3, similar to what is found for the distribution of price changes. The volatility distribution retains the same functional form for a range of values of T. Further, we study the volatility correlations by using the power spectrum analysis. Both methods support a power law decay of the correlation function and give consistent estimates of the relevant scaling exponents. Also, both methods show the presence of a crossover at approximately 1.5 days. In addition, we extend these results to the volatility of individual companies by analyzing a data base comprising all trades for the largest 500 U.S. companies over the two-year period Jan. 1994 to Dec. 1995.

Scaling for the critical percolation backbone

We study the backbone connecting two given sites of a two-dimensional lattice separated by an arbitrary distance r in a system of size L at the percolation threshold. We find a scaling form for the average backbone mass: <M(B)> approximately L(dB)G(r/L), where G can be well approximated by a power law for 0<or=x<or=1: G(x) approximately x(psi) with psi=0.37+/-0.02. This result implies that <M(B)> approximately L(dB-psi)r(psi) for the entire range 0<r<L. We also propose a scaling form for the probability distribution P(M(B)) of backbone mass for a given r. For r approximately L, P(MB) is peaked around L(dB), whereas for r<<L, P(M(B)) decreases as a power law, M(-tauB)B, with tauB approximately 1.20+/-0.03. The exponents psi and tauB satisfy the relation psi=dB(tauB-1), and psi is the codimension of the backbone, psi=d-dB.

Clustering of identical oligomers in coding and noncoding DNA sequences

We develop a quantitative method for analyzing repetitions of identical short oligomers in coding and noncoding DNA sequences. We analyze sequences presently available in the GenBank separately for primate, mammal, vertebrate, rodent, invertebrate and plant taxonomic partitions. We find that some oligomers "cluster" more than they would if randomly distributed, while other oligomers "repel" each other. To quantify this degree of clustering, we define clustering measures. We find that (i) clustering significantly differs in coding and noncoding DNA; (ii) in most cases, monomers, dimers and tetramers cluster in noncoding DNA but appear to repel each other in coding DNA. (iii) The degree of clustering for different sources (primates, invertebrates, and plants) is more conserved among these sources in the case of coding DNA than in the case of noncoding DNA. (iv) In contrast to other oligomers, we find that trimers always prefer to cluster. (v) Clustering of each particular oligomer is conserved within the same organism.

Dynamic feedback in an aggregation-disaggregation model

We study an aggregation-disaggregation model which is relevant to biological processes such as the growth of senile plaques in Alzheimer disease. In this model, during the aggregation each deposited particle has a probability of producing a new particle in its vicinity, while during disaggregation the particles are anihilated randomly. The model is held in a dynamic equilibrium by a feedback mechanism which changes the disaggregation probability in proportion to the change in the total number of particles. We also include surface diffusion which influences the morphology of growing aggregates and colonies. A colony includes the descendents of a single particle. We investigate the statistical properties of the model in two dimensions. We find that unlike the colonies, individual aggregates are fractals with a fractal dimension of D(f)=1.92+/-0.06 in the absence of surface diffusion. We show that the surface diffusion changes the fractal dimension of aggregates: at a small aggregation-disaggregation rate, D(f) is independent of the strength of the surface diffusion, D(f)=1.73+/-0.03. At larger aggregation-disaggregation rates and different strengths of surface diffusion, aggregates with fractal dimensions between D(f)=1.73 and 1.92 form. The steady-state distribution of aggregate sizes is shown to be power law if the aggregation-disaggregation process dominates over the surface diffusion. In the limit of weak aggregation-disaggregation and strong surface diffusion the size distribution is log-normal.

Statistical physics and physiology: monofractal and multifractal approaches

Even under healthy, basal conditions, physiologic systems show erratic fluctuations resembling those found in dynamical systems driven away from a single equilibrium state. Do such "nonequilibrium" fluctuations simply reflect the fact that physiologic systems are being constantly perturbed by external and intrinsic noise? Or, do these fluctuations actually, contain useful, "hidden" information about the underlying nonequilibrium control mechanisms? We report some recent attempts to understand the dynamics of complex physiologic fluctuations by adapting and extending concepts and methods developed very recently in statistical physics. Specifically, we focus on interbeat interval variability as an important quantity to help elucidate possibly non-homeostatic physiologic variability because (i) the heart rate is under direct neuroautonomic control, (ii) interbeat interval variability is readily measured by noninvasive means, and (iii) analysis of these heart rate dynamics may provide important practical diagnostic and prognostic information not obtainable with current approaches. The analytic tools we discuss may be used on a wider range of physiologic signals. We first review recent progress using two analysis methods--detrended fluctuation analysis and wavelets--sufficient for quantifying monofractual structures. We then describe recent work that quantifies multifractal features of interbeat interval series, and the discovery that the multifractal structure of healthy subjects is different than that of diseased subjects.

Structure of supercooled and glassy water under pressure

We use molecular-dynamics simulations to study the effect of temperature and pressure on the local structure of liquid water in parallel with neutron-scattering experiments. We find, in agreement with experimental results, that the simulated liquid structure at high pressure is nearly independent of temperature, and remarkably similar to the known structure of the high-density amorphous ice. Further, at low pressure, the liquid structure appears to approach the experimentally measured structure of low-density amorphous ice as temperature decreases. These results are consistent with the postulated continuity between the liquid and glassy phases of H2O.

Multifractality in human heartbeat dynamics

There is evidence that physiological signals under healthy conditions may have a fractal temporal structure. Here we investigate the possibility that time series generated by certain physiological control systems may be members of a special class of complex processes, termed multifractal, which require a large number of exponents to characterize their scaling properties. We report on evidence for multifractality in a biological dynamical system, the healthy human heartbeat, and show that the multifractal character and nonlinear properties of the healthy heart rate are encoded in the Fourier phases. We uncover a loss of multifractality for a life-threatening condition, congestive heart failure.

Avalanches in breakdown and fracture processes

We investigate the breakdown of disordered networks under the action of an increasing external-mechanical or electrical-force. We perform a mean-field analysis and estimate scaling exponents for the approach to the instability. By simulating two-dimensional models of electric breakdown and fracture we observe that the breakdown is preceded by avalanche events. The avalanches can be described by scaling laws, and the estimated values of the exponents are consistent with those found in mean-field theory. The breakdown point is characterized by a discontinuity in the macroscopic properties of the material, such as conductivity or elasticity, indicative of a first-order transition. The scaling laws suggest an analogy with the behavior expected in spinodal nucleation.

Plaque-induced neurite abnormalities: implications for disruption of neural networks in Alzheimer's disease

The brains of Alzheimer's disease patients contain extracellular Abeta amyloid deposits (senile plaques). Although genetic evidence causally links Abeta deposition to the disease, the mechanism by which Abeta disrupts cortical function is unknown. Using triple immunofluorescent confocal microscopy and three-dimensional reconstructions, we found that neuronal processes that cross through an Abeta deposit are likely to have a radically changed morphology. We modeled the electrophysiological effect of this changed morphology and found a predicted delay of several milliseconds over an average plaque. We propose that this type of delay, played out among thousands of plaques throughout neocortical areas, disrupts the precise temporal firing patterns of action potentials, contributing directly to neural system failure and dementia.

Dynamics of plaque formation in Alzheimer's disease

Plaques that form in the brains of Alzheimer patients are made of deposits of the amyloid-beta peptide. We analyze the time evolution of amyloid-beta deposition in immunostained brain slices from transgenic mice. We find that amyloid-beta deposits appear in clusters whose characteristic size increases from 14 microm in 8-month-old mice to 22 microm in 12-month-old mice. We show that the clustering has implications for the biological growth of amyloid-beta by presenting a growth model that accounts for the experimentally observed structure of individual deposits and predicts the formation of clusters of deposits and their time evolution.

Discrete molecular dynamics studies of the folding of a protein-like model

BACKGROUND

Many attempts have been made to resolve in time the folding of model proteins in computer simulations. Different computational approaches have emerged. Some of these approaches suffer from insensitivity to the geometrical properties of the proteins (lattice models), whereas others are computationally heavy (traditional molecular dynamics).

RESULTS

We used the recently proposed approach of Zhou and Karplus to study the folding of a protein model based on the discrete time molecular dynamics algorithm. We show that this algorithm resolves with respect to time the folding <--> unfolding transition. In addition, we demonstrate the ability to study the core of the model protein.

CONCLUSIONS

The algorithm along with the model of interresidue interactions can serve as a tool for studying the thermodynamics and kinetics of protein models.

Scaling features of noncoding DNA

We review evidence supporting the idea that the DNA sequence in genes containing noncoding regions is correlated, and that the correlation is remarkably long range--indeed, base pairs thousands of base pairs distant are correlated. We do not find such a long-range correlation in the coding regions of the gene, and utilize this fact to build a Coding Sequence Finder Algorithm, which uses statistical ideas to locate the coding regions of an unknown DNA sequence. Finally, we describe briefly some recent work adapting to DNA the Zipf approach to analyzing linguistic texts, and the Shannon approach to quantifying the "redundancy" of a linguistic text in terms of a measurable entropy function, and reporting that noncoding regions in eukaryotes display a larger redundancy than coding regions. Specifically, we consider the possibility that this result is solely a consequence of nucleotide concentration differences as first noted by Bonhoeffer and his collaborators. We find that cytosine-guanine (CG) concentration does have a strong "background" effect on redundancy. However, we find that for the purine-pyrimidine binary mapping rule, which is not affected by the difference in CG concentration, the Shannon redundancy for the set of analyzed sequences is larger for noncoding regions compared to coding regions.