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PubMed1996

Evidence for nonrandom hydrophobicity structures in protein chains.

The question of whether proteins originate from random sequences of amino acids is addressed. A statistical analysis is performed in terms of blocked and random walk values formed by binary hydrophobic assignments of the amino acids along the protein chains. Theoretical expectations of these variables from random distributions of hydrophobicities are compared with those obtained from functional proteins. The results, which are based upon proteins in the SWISS-PROT data base, convincingly show that the amino acid sequences in proteins differ from what is expected from random sequences in a statistically significant way. By performing Fourier transforms on the random walks, one obtains additional evidence for nonrandomness of the distributions. We have also analyzed results from a synthetic model containing only two amino acid types, hydrophobic and hydrophilic. With reasonable criteria on good folding properties in terms of thermodynamical and kinetic behavior, sequences that fold well are isolated. Performing the same statistical analysis on the sequences that fold well indicates similar deviations from randomness as for the functional proteins. The deviations from randomness can be interpreted as originating from anticorrelations in terms of an Ising spin model for the hydrophobicities. Our results, which differ from some previous investigations using other methods, might have impact on how permissive with respect to sequence specificity protein folding process is-only sequences with nonrandom hydrophobicity distributions fold well. Other distributions give rise to energy landscapes with poor folding properties and hence did not survive the evolution.

Databases, Factual↗
PubMed1991

Chemotactic movement of single cells.

Two central features of polymorphonuclear neutrophil leukocyte chemosensory movement behavior demand fundamental theoretical understanding. In uniform concentrations of chemoattractant, neutrophils exhibit a persistent random walk, with a characteristic directional persistence time between significant changes in direction. In attractant concentration gradients, they demonstrate a biased random walk, with an orientation bias characterizing the fraction of cells moving up the gradient. A coherent picture of cell movement responses to attractant requires that both persistence and bias be explained within a unifying framework. We offer the hypothesis that "noise" in the cellular chemical signal detection/response process can simultaneously account for these two key phenomena. In particular, we develop a stochastic mathematical model for cell chemosensory movement based on kinetic fluctuations in attractant-receptor binding. This model is capable of simulating cell paths observed experimentally in uniform concentrations as well as concentration gradients. It also quantitatively predicts both persistence time in uniform attractant concentrations and orientation bias in gradients, and the predictions compare favorably to data for neutrophils responding to chemotactic peptide. Further, the model analysis elucidates how persistence time and orientation bias depend on the model parameters associated with receptor binding, receptor signal transduction, and the cell turning response. Thus, the concept of signal "noise" can quantitatively unify the major characteristics of leukocyte random motility and chemotaxis. The same level of noise large enough to account for the observed frequency of turning in uniform environments is simultaneously small enough to allow for the observed degree of directional bias in gradients.

Animals↗
PubMed1993

Lateral diffusion in an archipelago. Single-particle diffusion.

Several laboratories have measured lateral diffusion of single particles on the cell surface, and these measurements may reveal an otherwise inaccessible level of submicroscopic organization of cell membranes. Pitfalls in the interpretation of these experiments are analyzed. Random walks in unobstructed systems show structure that could be interpreted as free diffusion, obstructed diffusion, directed motion, or trapping in finite domains. To interpret observed trajectories correctly, one must consider not only the trajectories themselves but also the probabilities of occurrence of various trajectories. Measures of the asymmetry of obstructed and unobstructed random walks are calculated, and probabilities are evaluated for random trajectories that resemble either directed motion or diffusion in a bounded region.

Cell Membrane↗
PubMed2005

How large is an alpha-helix? Studies of the radii of gyration of helical peptides by small-angle X-ray scattering and molecular dynamics.

Using synchrotron radiation and the small-angle X-ray scattering technique we have measured the radii of gyration of a series of alanine-based alpha-helix-forming peptides of the composition Ace-(AAKAA)(n)-GY-NH(2), n=2-7, in aqueous solvent at 10(+/-1) degrees C. In contrast to other techniques typically used to study alpha-helices in isolation (such as nuclear magnetic resonance and circular dichroism), small-angle X-ray scattering reports on the global structure of a molecule and, as such, provides complementary information to these other, more sequence-local measuring techniques. The radii of gyration that we measure are, except for the 12-mer, lower than the radii of gyration of ideal alpha-helices or helices with frayed ends of the equivalent sequence-length. For example, the measured radius of gyration of the 37-mer is 14.2(+/-0.6)A, which is to be compared with the radius of gyration of an ideal 37-mer alpha-helix of 17.6A. Attempts are made to analyze the origin of this discrepancy in terms of the analytical Zimm-Bragg-Nagai (ZBN) theory, as well as distributed computing explicit solvent molecular dynamics simulations using two variants of the AMBER force-field. The ZBN theory, which treats helices as cylinders connected by random walk segments, predicts markedly larger radii of gyration than those measured. This is true even when the persistence length of the random walk parts is taken to be extremely short (about one residue). Similarly, the molecular dynamics simulations, at the level of sampling available to us, give inaccurate values of the radii of gyration of the molecules (by overestimating them by around 25% for longer peptides) and/or their helical content. We conclude that even at the short sequences examined here (< or =37 amino acid residues), these alpha-helical peptides behave as fluctuating semi-broken rods rather than straight cylinders with frayed ends.

Circular Dichroism↗
PubMed1997

Regional differences in the compaction of chromatin in human G0/G1 interphase nuclei.

The large-scale structure of chromatin corresponding to G- and R-bands in human G0/G1 interphase nuclei was compared. Fluorescence in situ hybridization (FISH) was used to measure the interphase distance between 42 pairs of probes separated by 0.1-1.5 Mbp. The probe pairs were derived from 21q22.2 and Xp21.3, G-band positive regions, and from 4p16.3, 6p21.3, and Xq28, R-band positive regions. Distributions of measured interphase distances in all regions approximated a Rayleigh distribution, suggesting that the chromatin follows a random-walk path over this range. A linear correlation of mean-square interphase distance and genomic separation, also indicative of random-walk folding, was observed in all regions. The slope of the correlation observed using probes from G-band regions was systematically lower than that from R-band regions. The difference in the slope between Xp21.3 and Xq28 was particularly striking and was observed in normal fibroblast cells, fixed alternatively with methanol and acetic acid or paraformaldehyde, and HeLa cells. These results demonstrate regional differences in large-scale chromosome structure during interphase, with the more openly configured chromatin corresponding to R-bands.

Chromatin↗
PubMed2005

Low-temperature dynamics of kinks on Ising interfaces.

The anisotropic motion of an interface driven by its intrinsic curvature or by an external field is investigated in the context of the kinetic Ising model in both two and three dimensions. We derive in two dimensions (2D) a continuum evolution equation for the density of kinks by a time-dependent and nonlocal mapping to the asymmetric exclusion process. Whereas kinks execute random walks biased by the external field and pile up vertically on the physical 2D lattice, they execute hard-core biased random walks on a transformed 1D lattice. Their density obeys a nonlinear diffusion equation which can be transformed into the standard expression for the interface velocity, v=M [ (gamma+gamma'') kappa+H] , where M , gamma+gamma", and kappa are the interface mobility, stiffness, and curvature, respectively. In 3D, we obtain the velocity of a curved interface near the 100 orientation from an analysis of the self-similar evolution of 2D shrinking terraces. We show that this velocity is consistent with the one predicted from the 3D tensorial generalization of the law for anisotropic curvature-driven motion. In this generalization, both the interface stiffness tensor and the curvature tensor are singular at the 100 orientation. However, their product, which determines the interface velocity, is smooth. In addition, we illustrate how this kink-based kinetic description provides a useful framework for studying more complex situations by modeling the effect of immobile dilute impurities.

Journal Article↗
PubMed2003

Lévy flights in inhomogeneous media.

We investigate the impact of external periodic potentials on superdiffusive random walks known as Lévy flights and show that even strongly superdiffusive transport is substantially affected by the external field. Unlike ordinary random walks, Lévy flights are surprisingly sensitive to the shape of the potential while their asymptotic behavior ceases to depend on the Lévy index mu. Our analysis is based on a novel generalization of the Fokker-Planck equation suitable for systems in thermal equilibrium. Thus, the results presented are applicable to the large class of situations in which superdiffusion is caused by topological complexity, such as diffusion on folded polymers and scale-free networks.

Journal Article↗
PubMed2004

Average trajectory of returning walks.

We compute the average shape of trajectories of some one-dimensional stochastic processes x(t) in the (t,x) plane during an excursion, i.e., between two successive returns to a reference value, finding that it obeys a scaling form. For uncorrelated random walks the average shape is semicircular, independent from the single increments distribution, as long as it is symmetric. Such universality extends to biased random walks and Levy flights, with the exception of a particular class of biased Levy flights. Adding a linear damping term destroys scaling and leads asymptotically to flat excursions. The introduction of short and long ranged noise correlations induces nontrivial asymmetric shapes, which are studied numerically.

Journal Article↗
PubMed2004

The variance reaction time model.

The variance reaction time model (VRTM) is proposed to account for various recognition data on reaction time, the mirror effect, receiver-operating-characteristic (ROC) curves, etc. The model is based on simple and plausible assumptions within a neural network: VRTM is a two layer neural network where one layer represents items and one layer represents contexts. The recognition decision is based on a random walk of nodes activated at recognition. VRTM suggests theoretical constraints on the distributions of nodes activated at recognition and the noise in the random walk. The variability in the net inputs to nodes depends on the item frequency (the number of times that the item has been encoded) and the list length. The essential mechanism that accounts for the empirical data is a non-linear activation function. The mean activation threshold in the non-linear activation function is placed to achieve efficient discriminability between new and old items and there is variability in the activation threshold. VRTM predicts the mirror effect for low and high frequency words, a strength based mirror effect between conditions but not within one condition, appropriate ROC-curves for old/new and high/low frequency items, and list-length effects. Furthermore, it predicts appropriate means and distributions of reaction times for old/new, correct/incorrect, and high/low frequency items as well as speed/accuracy tradeoffs. VRTM has an explicit mathematical solution, it is simulated in a neural network, and it is fitted to a number of datasets.

Attention↗
PubMed2002

Deterministic diffusion in flower-shaped billiards.

We propose a flower-shaped billiard in order to study the irregular parameter dependence of chaotic normal diffusion. Our model is an open system consisting of periodically distributed obstacles in the shape of a flower, and it is strongly chaotic for almost all parameter values. We compute the parameter dependent diffusion coefficient of this model from computer simulations and analyze its functional form using different schemes, all generalizing the simple random walk approximation of Machta and Zwanzig. The improved methods we use are based either on heuristic higher-order corrections to the simple random walk model, on lattice gas simulation methods, or they start from a suitable Green-Kubo formula for diffusion. We show that dynamical correlations, or memory effects, are of crucial importance in reproducing the precise parameter dependence of the diffusion coefficent.

Journal Article↗
PubMed2005

Fast flat-histogram method for generalized spin models.

We present a Monte Carlo method that efficiently computes the density of states for spin models having any number of interaction per spin. By combining a random walk in the energy space with collective updates controlled by the microcanonical temperature, our method yields dynamic exponents close to their ideal random-walk values, reduced equilibrium times, and very low statistical error in the density of states. The method can host any density of states estimation scheme, including the Wang-Landau algorithm and the transition matrix method. Our approach proves remarkably powerful in the numerical study of models governed by long-range interactions, where it is shown to reduce the algorithm complexity to that of a short-range model with the same number of spins. We apply the method to the -state Potts chains with power-law decaying interactions in their first-order regime; we find that conventional local-update algorithms are outperformed already for sizes above a few hundred spins. By considering chains containing up to spins, which we simulated in fairly reasonable time, we obtain estimates of transition temperatures correct to five-figure accuracy. Finally, we propose several efficient schemes aimed at estimating the microcanonical temperature.

Journal Article↗
PubMed2000

Lévy flights from a continuous-time process.

Lévy flight dynamics can stem from simple random walks in a system whose operational time (number of steps n) typically grows superlinearly with physical time t. Thus this process is a kind of continuous-time random walk (CTRW), dual to the typical Scher-Montroll model, in which n grows sublinearly with t. Models in which Lévy flights emerge due to a temporal subordination allow one easily to discuss the response of a random walker to a weak outer force, which is shown to be nonlinear. On the other hand, the relaxation of an ensemble of such walkers in a harmonic potential follows a simple exponential pattern, and leads to a normal Boltzmann distribution. Mixed models, describing normal CTRW's in superlinear operational time and Lévy flights under the operational time of subdiffusive CTRW's lead to a paradoxical diffusive behavior, similar to the one found in transport on polymer chains. The relaxation to the Boltzmann distribution in such models is slow, and asymptotically follows a power law.

Journal Article↗
PubMed1996

Efficiency of separation of DNA mutations by constant denaturant capillary electrophoresis is controlled by the kinetics of DNA melting equilibrium.

Constant denaturant capillary electrophoresis (CDCE) separation takes place in the heated portion of the capillary where faster-moving, unmelted DNA fragments are in equilibrium with slower-moving, partially melted forms. Within a certain temperature range, the position of the melting equilibrium and thus the average electrophoretic mobility of each mutant is different. The resulting differences in mobility allow sequences containing single base pair point mutations to be separated from each other. We report the results of experiments in which we explored the rules defining separation efficiency by varying the parameters of CDCE. We discovered an unusual peak broadening mechanism. In contrast to most other DNA electrophoresis systems, peak width in CDCE steadily decreases with the square root of the separation speed. Moreover, the peak width displays a sharp maximum at a specific temperature. To account for these observations, we use a model which describes CDCE separation as a random walk. According to this model, peaks in CDCE are broad because the kinetics of the melting equilibrium are slow and therefore the number of random walk steps represented by melting/renaturation transitions is relatively small. In addition to providing a satisfactory interpretation of the data, the model also predicts that separation efficiency will increase as the ionic strength of the running buffer is increased and as the concentration of denaturant in the buffer is decreased. These predictions were verified and were used to establish conditions for high-resolution CDCE suitable for separating complex mixtures of single base pair mutants.

Buffers↗
PubMed1980

A stochastic model for oviductal egg transport.

A mathematical description of ovum transport based on Langevin's diffusion equation is presented. The proposed model is deduced from qualitative features of this phenomenon, not induced from numerical fitting of experimental data. We demonstrate that egg transport in the ampulla of the rabbit oviduct can be represented as a one-dimensional random walk in a field of external force. The application of the model to describe isthmic ovum and sperm transport on the basis of simple random walk process is also discussed. The present formulation identifies and characterizes the forces involved in the motions of the ovum and predicts specific alternatives for physiological regulation of egg transport in the oviduct.

Animals↗
PubMed1999

Contribution of plus and minus end pathways to microtubule turnover.

Turnover is important for the maintenance and remodeling of the cytoskeleton during the processes of cell morphogenesis, mitosis and motility. Microtubule (MT) turnover is thought to occur by dynamic instability, growth and shortening at distal (plus) ends. Recent observation of MT release from the centrosome and depolymerization from proximal (minus) ends indicates the existence of a minus end pathway. To evaluate the relative contributions of plus and minus end pathways to turnover, we analyzed MT dynamics in a model system, the fish melanophore, a large non-motile cell with a regular radial array of long MTs. MT ends were tracked in digital fluorescence time-lapse sequences and life histories of individual MTs were analyzed using random walk theory generalized to the case of diffusion with drift. Analysis of plus end dynamics gave an apparent diffusion coefficient of D=7.5 microm2/minute. The random walk model predicts that the half-time for turnover driven solely by plus end dynamics will depend strongly on position in the cell. Based on the experimentally determined value of D, turnover of MTs near the center of a typical melanophore of radius 70 microm was calculated to require over 5 hours, a paradoxically long time. To examine MT behavior deep in the cytoplasm, we developed a novel, sequential subtraction mode of image analysis. This analysis revealed a subpopulation of MTs which shortened from their minus ends, presumably after constitutive release from the centrosome. Given the relative slowness of plus end dynamics to turn over the root of a long MT, the turnover of MTs near the cell center is determined primarily by the minus-end pathway. MTs released from the centrosome become replaced by newly nucleated ones. The relative contributions of plus and minus end pathways was estimated from the diffusion coefficient, D, for the plus end, the length distribution of MTs, t he frequency of free minus ends, and the rate of minus-end shortening. We conclude that, in large animal cells with a centrosomally focussed array of MTs, turnover occurs by a combination of plus and minus end pathways, the plus end dominating at the cell periphery and the minus end dominating near the cell center.

Animals↗
PubMed2003

Diffusive-ballistic crossover in 1D quantum walks.

We show that particle transport, as characterized by the equilibrium mean square displacement, in a uniform, quantum multibaker map, is generically ballistic in the long time limit, for any fixed value of Planck's constant. However, for fixed times, the semiclassical limit leads to diffusion. Random matrix theory provides explicit analytical predictions for the mean square displacement of a particle in the system. These results exhibit a crossover from diffusive to ballistic motion, with crossover time on the order of the inverse of Planck's constant. We expect that, for a large class of 1D quantum random walks similar to the quantum multibaker, a sufficient condition for diffusion in the semiclassical limit is classically chaotic dynamics in each cell. The systems described generalize known quantum random walks and may have applications for quantum computation.

Journal Article↗
PubMed1992

Analysis of diffusional broadening of vesicular packets of catecholamines released from biological cells during exocytosis.

Secretion of catecholamines is observed as a series of current spikes when measured at the surface of a bovine adrenal medullary cell in culture with a carbon-fiber microelectrode operated in the amperometric mode. Prior work has shown that these spikes are due to detection of concentrated packets of catecholamines which are released from individual vesicles after their fusion with the cell membrane, a process known as exocytosis. The shape of the individual current spikes, detected with a 5-microns spacing between the hemispherical cell and the electrode, has been compared to the shape generated by a theoretical model. The model consists of an instantaneous point source of material on a surface which subsequently diffuses to a disk that consumes the emitted material. The pertinent diffusion conditions have been evaluated with finite difference and random walk digital simulations. The two methods give identical results when the point source is located on a plane. The more realistic simulation geometry, emission from a hemispherical surface, was evaluated with the random walk method. The simulations allow a set of criteria to be established to evaluate diffusion-controlled broadening of spike shape. The broad range of spike widths observed experimentally and their individual shapes measured with 5-microns cell-electrode spacing are consistent with diffusion from point sources randomly distributed across a hemispherical surface. The data can be described with the diffusion coefficient for catecholamines in free solution. The model enables evaluation of signal-to-noise losses and correction for diffusional losses which are dependent on electrode radius.(ABSTRACT TRUNCATED AT 250 WORDS)

Animals↗
PubMed2006

Computer simulation of electrical conductivity of colloidal dispersions during aggregation.

The computation approach to the simulation of electrical conductivity of colloidal dispersions during aggregation is considered. We use the two-dimensional diffusion-limited aggregation model with multiple-seed growth. The particles execute a random walk, but lose their mobility after contact with the growing clusters or seeds. The two parameters that control the aggregation are the initial concentration of free particles in the system p and the concentration of seeds psi. The case of psi=1, when all the particles are the immobile seeds, corresponds with the usual random percolation problem. The other limiting case of psi=0, when all the particles walk randomly, corresponds to the dynamical percolation problem. The calculation of electrical conductivity and cluster analysis were done with the help of the algorithms of Frank-Lobb and Hoshen-Kopelman. It is shown that the percolation concentration phi c decreases from 0.5927 at psi=1 to 0 at psi --> 0. Scaling analysis was applied to study exponents of correlation length v and of conductivity t. For all psi>0 this model shows universal behavior of classical 2d random percolation with v approximately t approximately 4/3. The electrical conductivity sigma of the system increases during aggregation reaching up to a maximum at the final stage. The concentration dependence of conductivity sigma(phi) obeys the general effective medium equation with apparent exponent ta(psi) that exceeds t. The kinetics of electrical conductivity changes during the aggregation is discussed. In the range of concentration Pc(phi)<p<0.9527 the time of percolation cluster formation pi c decreases with increasing phi.

Journal Article↗