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PubMed2002

Random walk models of worker sorting in ant colonies.

Sorting can be an important mechanism for the transfer of information from one level of biological organization to another. Here we study the algorithm underlying worker sorting in Leptothorax ant colonies. Worker sorting is related to task allocation and therefore to the adaptive advantages associated with an efficient system for the division of labour in ant colonies. We considered four spatially explicit individual-based models founded on two-dimensional correlated random walk. Our aim was to establish whether sorting at the level of the worker population could occur with minimal assumptions about the behavioural algorithm of individual workers. The behaviour of an individual worker in the models could be summarized by the rule "move if you can, turn always". We assume that the turning angle of a worker is individually specific and negatively dependent on the magnitude of an internal parameter micro which could be regarded as a measure of individual experience or task specialization. All four models attained a level of worker sortedness that was compatible with results from experiments onLeptothorax ant colonies. We found that the presence of a sorting pivot, such as the nest wall or an attraction force towards the centre of the worker population, was crucial for sorting. We make a distinction between such pivots and templates and discuss the biological implications of their difference.

Algorithms↗
PubMed2002

Transport of fallout radiocesium in the soil by bioturbation: a random walk model and application to a forest soil with a high abundance of earthworms.

It is well known that bioturbation can contribute significantly to the vertical transport of fallout radionuclides in grassland soils. To examine this effect also for a forest soil, activity-depth profiles of Chernobyl-derived 134Cs from a limed plot (soil, hapludalf under spruce) with a high abundance of earthworms (Lumbricus rubellus) in the Olu horizon (thickness=3.5 cm) were evaluated and compared with the corresponding depth profiles from an adjacent control plot. For this purpose, a random-walk based transport model was developed, which considers (i) the presence of an initial activity-depth distribution, (ii) the deposition history of radiocesium at the soil surface, (iii) individual diffusion/dispersion coefficients and convection rates for the different soil horizons, and (iv) mixing by bioturbation within one soil horizon. With this model, the observed 134Cs-depth distribution at the control site (no bioturbation) and at the limed site could be simulated quite satisfactorily. It is shown that the observed, substantial long-term enrichment of 134Cs in the bioturbation horizon can be modeled by an exceptionally effective diffusion process, combined with a partial reflection of the randomly moving particles at the two borders of the bioturbation zone. The present model predicts significantly longer residence times of radiocesium in the organic soil layer of the forest soil than obtained from a first-order compartment model, which does not consider bioturbation explicitly.

Animals↗
PubMed1979

Dynamics of technological evolution: Random walk model for the research enterprise.

Technological evolution is a consequence of a sequence of replacements. The development of a new technology generally follows from model testing of the basic ideas on a small scale. Traditional technologies such as aerodynamics and naval architecture involved feasibility experiments on systems characterized by only one or two dimensionless constants. Technologies of the "future" such as magnetically confined fusion depend upon many coupled dimensionless constants. Research and development is modeled and analyzed in terms of random walks in appropriate dimensionless constant space.

Journal Article↗
PubMed2005

From random walk to single-file diffusion.

We report an experimental study of diffusion in a quasi-one-dimensional (q1D) colloid suspension which behaves like a Tonks gas. The mean squared displacement as a function of time is described well with an ansatz encompassing a time regime that is both shorter and longer than the mean time between collisions. The ansatz asserts that the inverse mean squared displacement is the sum of the inverse mean squared displacement for short time normal diffusion (random walk) and the inverse mean squared displacement for asymptotic single-file diffusion (SFD). The dependence of the 1D mobility in the SFD on the concentration of the colloids agrees quantitatively with that derived for a hard rod model, which confirms for the first time the validity of the hard rod SFD theory. We also show that a recent SFD theory by Kollmann leads to the hard rod SFD theory for a Tonks gas.

Journal Article↗
PubMed2005

Random-walk statistics in moment-based O(N) tight binding and applications in carbon nanotubes.

A computational framework for a moment-based O(N) tight-binding atomistic method is presented, analyzed, and applied to the problem of electronic properties of deformed carbon nanotubes, where N is the number of atoms in the system. The moment-based approach is based on the maximum entropy and kernel polynomial methods for constructing the electronic density of states from local statistical information about the environment around individual atoms. Random-walk statistics are formally presented as the basis for several methods to collect the moments of the density of states in a computationally efficient manner. The computational complexity and accuracy of these methods are systematically analyzed. Using these methods for the problem of deformed carbon nanotubes, it is shown that the computational cost for some cases, per atom, scales as efficiently as O(M log M), where M is the desired number of moments in the expansion of the density of states. These methods are compared to other methods such as direct diagonalization and a Green's function approach.

Journal Article↗
PubMed1979

Self-avoiding random walks at finite concentrations: The bulk phase limit.

In infinitely dilute solutions, macromolecules exhibit non-Gaussian distributions for their end-to-end separations. This occurs under such circumstances because intramolecular interactions are more important than intermolecular forces. On the other hand, when a macromolecular solution becomes so concentrated that it approaches its bulk phase, then the end-to-end length distribution becomes substantially Gaussian. A theoretical explanation for the observed behavior is obtained by taking cognizance of a balance between inter-and intramolecular forces acting on self-avoiding random chains. Such a balance causes the chains to behave very much like random walks of order 2-that is to say, walks for which the only restriction against double occupancy is that identified with immediate return steps. This is demonstrated by taking Monte Carlo data for chains of various concentrations and analyzing the distributions of a component of length by using expansions involving orthogonal vectors. Although Gaussian behavior is more or less achieved for bulk polymers, slight deviations from that behavior still persist at the origin.

Journal Article↗
PubMed2002

Diffusion of volatile compounds in fibre networks: experiments and modelling by random walk simulation.

Predictive migration models for polymers are already so well established that the European Commission intends to allow the use of the models as one quality assurance tool in product safety assessment of plastic materials and articles for food contact. The inhomogeneity of fibre-based materials makes modelling difficult--thus, little research has been done in this area. The authors compare experiments on the diffusion of certain volatile compounds through laboratory kraft pulp sheets with computer simulations in which the fibre network structure is modelled explicitly. The major advantage of the present random walk simulation is that it gives an estimate of the effective diffusion constant for the fibre network. For most compounds, the agreement between the experiments and simulations is good. The experiments and simulations indicate that gas diffusion rate is very sensitive to sheet porosity.

Diffusion↗
PubMed1991

A random walk method for computing genetic location scores.

Calculation of location scores is one of the most computationally intensive tasks in modern genetics. Since these scores are crucial in placing disease loci on marker maps, there is ample incentive to pursue such calculations with large numbers of markers. However, in contrast to the simple, standardized pedigrees used in making marker maps, disease pedigrees are often graphically complex and sparsely phenotyped. These complications can present insuperable barriers to exact likelihood calculations with more than a few markers simultaneously. To overcome these barriers we introduce in the present paper a random walk method for computing approximate location scores with large numbers of biallelic markers. Sufficient mathematical theory is developed to explain the method. Feasibility is checked by small-scale simulations for two applications permitting exact calculation of location scores.

Chromosome Walking↗
PubMed1979

On two-dimensional passive random walk in lipid bilayers and fluid pathways in biomembranes.

The lateral mobility of pyrene, pyrene decanoic acid, and 1-palmitoyl-2-pyrene decanoyl-phosphatidyl choline (pyrene lecithin) in lipid bilayers is determined by the excimer formation technique. This method is applied to vesicles of lecithins differing in chain length and in the degree of saturation of the hydrocarbon chains. These values are compared with results in cephalins of different chain length and in dipalmitoyl phosphatidic acid at variable pH. The influence of cholesterol is investigated. The results are analyzed in terms of the Montroll model of two-dimensional random walk. The jump frequency of the probe molecule within the lipid lattice is obtained. The advantage of this measure of transport in lipid layers is that it does not involve lipid lattice parameters. The main results of the present work are: (i) The lateral mobility of a given solute molecule in lamellae of saturated lecithins is independent of hydrocarbon chain length and rather a universal function of temperature. (ii) In unsaturated dioleyl lecithin the amphiphatic molecules have lateral mobilities of the same size as in saturated lipids. The jump frequency of pyrene, however, is by a factor of two larger in the unsaturated lecithin. (iii) The jump frequencies in phosphatidyl ethanolamines are about equal to those in lecithins. (iv) In phosphatidic acid layers the hopping frequencies depend on the charges of the head groups of both the lipids and the probes. (v) Cholesterol strongly reduces the jump frequency in fluid layers. (vi) The lateral mobility in biological membranes is comparable to that in artificial lipid bilayers. The experimental results are discussed in terms of the free volume model of diffusion in fluids. Good agreement with the predictions made from this model is found. A striking result is the observation of a tilt in dioleyl-lecithin bilayer membranes from the hopping frequencies of pyrene and pyrene lecithin. A tilt angle of phi = 17 degrees is estimated.

Cholesterol↗
PubMed2003

Chain conformation in thin polymer layers as revealed by simulations of ideal random walks.

A confinement-induced mode was discovered in thin cis-1,4-polyisoprene (PI) layers if the film thickness becomes comparable with the size of the PI coil (A. Serghei, F. Kremer, to be published in Phys. Rev. Lett.). It was assigned to the fluctuation of the terminal subchains which are formed by the immobilization of chain segments at the contact with a confining interface. In the present paper we discuss the results of simulations done in order to gain an additional insight into the nature of this novel relaxation process. It turns out that the simulations of the chains as pinned random walks reproduce most of the essential features observed in the experiment.

Journal Article↗
PubMed2005

Evaluation of data in terms of two-dimensional random walk model: interaction between NADH-cytochrome b5 reductase and cytochrome b5.

Normally, bimolecular reactions are analyzed in terms of the Smoluchowski theory. However, when one attempts to generalize this analysis to cases where diffusion proceeds in two other than in three dimensions, one soon encounters severe conceptual difficulties. Although kinetic studies of membrane enzymes are generally difficult because the usual kinetic formalism refers to nonaggregated homogenous solutions, a major goal of our research is to define the molecular mechanism(s) by which alterations in membrane-bound substrate contents affect the enzyme activity in the same membrane. For that purpose, a simplified random-walk model was adopted in the present work. The enzyme reaction in the two-dimensional membrane could be calculated theoretically by applying the classical analysis of heat equation. As a result, the theoretical rate equation well accounting experimental findings was derived on the model of the liver microsomal NADH-cytochrome b5 reductase reaction. Furthermore, it was found that the modification of the simple rigid-sphere collision theory by including a term called the steric factor was not necessary in this derived equation.

Animals↗
PubMed2003

Interpretation of out-diffusion experiments on crystalline rocks using random walk modeling.

Matrix diffusion in saturated rocks with very low permeability is one of the major mechanisms of solute transport. Laboratory out-diffusion experiments on rock samples may provide an estimate of the bulk diffusion coefficient. However, numerous results have shown that this average parameter does not really depict the complex mechanism of diffusion as a function of the internal heterogeneity of crystalline rocks. Two-dimensional images of the porosity distribution in a granite sample were obtained by impregnation with a radioactive resin and autoradiography. Some examples based on these images and synthetic images were used to perform numerical simulations of out-diffusion using two different random walk methods. The simulated shapes of the out-diffusion curves depend on the spatial distribution of the porosity and on the pore connectivity with the border of the sample. Such relations might explain the multiple nested slopes or the convex shapes often observed on real experimental curves.

Diffusion↗
PubMed1996

NMR-based, molecular dynamics- and random walk molecular mechanics-supported study of conformational aspects of a carbohydrate ligand (Gal beta 1-2Gal beta 1-R) for an animal galectin in the free and in the bound state.

The binding of a carbohydrate to a lectin may affect the conformation of the ligand. To address this question for the galectin from chicken liver, the conformation of Gal beta 1-2Gal beta 1-R was analyzed in the free and in the galectin-bound state with 2D-ROESY- and 1D- as well as 2D-transferred NOE-experiments. A computer-assisted analysis of spatial parameters of the ligand by molecular dynamics (MD) and random walk molecular mechanics (RAMM) calculations, taking different dielectric constraints from epsilon = 1 to epsilon = 80 and various force fields into account, were instrumental to define the energetic minima of the free state. NMR-derived interresidual distance constraints enabled a conformational mapping. The two overlapping interresidual distance constraints obtained from transferred-NOE experiments of the galectin-ligand complex clearly support the notion that the conformation of the disaccharide in the bound state is at least very close to its global energy minimum state in solution.

Animals↗
PubMed2005

Random walk models for bayesian clustering of gene expression profiles.

The analysis of gene expression temporal profiles is a topic of increasing interest in functional genomics. Model-based clustering methods are particularly interesting because they are able to capture the dynamic nature of these data and to identify the optimal number of clusters. We have defined a new Bayesian method that allows us to cope with some important issues that remain unsolved in the currently available approaches: the presence of time dislocations in gene expression, the non-stationarity of the processes generating the data, and the presence of data collected on an irregular temporal grid. Our method, which is based on random walk models, requires only mild a priori assumptions about the nature of the processes generating the data and explicitly models inter-gene variability within each cluster. It has first been validated on simulated datasets and then employed for the analysis of a dataset relative to serum-stimulated fibroblasts. In all cases, the results have been promising, showing that the method can be helpful in functional genomics research.

Journal Article↗
PubMed2003

Temporal dynamics of recurrent airway symptoms and cellular random walk.

Asthma is a complex chronic inflammatory disease of the small airways that has dramatically increased in prevalence in industrialized countries during the last decades. Risk factors for adult asthma have been related to the complex array of gene-environment interactions and exposure of the immune system to allergens in early childhood. In genetically predisposed subjects, continuous exposure to environmental agents such as allergens or infections can lead to recurrent airway symptoms characterized by recurrent episodes of airway inflammation and bronchoconstriction with clinical symptoms of cough, dyspnea, or wheezing. In this study, we report that the longterm temporal dynamics of recurrent airway symptoms in a population of unselected infants display a complex intermittent pattern and that the distribution of interepisode intervals follows a power law. We interpret the data by using a model of the dynamics of attack episodes in which an attack is triggered by an avalanche of airway constrictions. We map the dynamics of this model to the known problem of a random walk in the presence of an absorbing boundary in which the walker corresponds to the fluctuations in contractile state of airway smooth muscle cells. These findings may provide new insight into the mechanisms of otherwise unexplained symptom episodes.

Asthma↗
PubMed2005

Combining the meiosis Gibbs sampler with the random walk approach for linkage and association studies with a general complex pedigree and multimarker loci.

A linkage analysis for finding inheritance states and haplotype configurations is an essential process for linkage and association mapping. The linkage analysis is routinely based upon observed pedigree information and marker genotypes for individuals in the pedigree. It is not feasible for exact methods to use all such information for a large complex pedigree especially when there are many missing genotypic data. Proposed Markov chain Monte Carlo approaches such as a single-site Gibbs sampler or the meiosis Gibbs sampler are able to handle a complex pedigree with sparse genotypic data; however, they often have reducibility problems, causing biased estimates. We present a combined method, applying the random walk approach to the reducible sites in the meiosis sampler. Therefore, one can efficiently obtain reliable estimates such as identity-by-descent coefficients between individuals based on inheritance states or haplotype configurations, and a wider range of data can be used for mapping of quantitative trait loci within a reasonable time.

Computer Simulation↗
PubMed2002

Diffusion of epicenters of earthquake aftershocks, Omori's law, and generalized continuous-time random walk models.

The epidemic-type aftershock sequence (ETAS) model is a simple stochastic process modeling seismicity, based on the two best-established empirical laws, the Omori law (power-law decay approximately 1/t(1+theta) of seismicity after an earthquake) and Gutenberg-Richter law (power-law distribution of earthquake energies). In order to describe also the space distribution of seismicity, we use in addition a power-law distribution approximately 1/r(1+mu) of distances between triggered and triggering earthquakes. The ETAS model has been studied for the last two decades to model real seismicity catalogs and to obtain short-term probabilistic forecasts. Here, we present a mapping between the ETAS model and a class of CTRW (continuous time random walk) models, based on the identification of their corresponding master equations. This mapping allows us to use the wealth of results previously obtained on anomalous diffusion of CTRW. After translating into the relevant variable for the ETAS model, we provide a classification of the different regimes of diffusion of seismic activity triggered by a mainshock. Specifically, we derive the relation between the average distance between aftershocks and the mainshock as a function of the time from the mainshock and of the joint probability distribution of the times and locations of the aftershocks. The different regimes are fully characterized by the two exponents theta and mu. Our predictions are checked by careful numerical simulations. We stress the distinction between the "bare" Omori law describing the seismic rate activated directly by a mainshock and the "renormalized" Omori law taking into account all possible cascades from mainshocks to aftershocks of aftershock of aftershock, and so on. In particular, we predict that seismic diffusion or subdiffusion occurs and should be observable only when the observed Omori exponent is less than 1, because this signals the operation of the renormalization of the bare Omori law, also at the origin of seismic diffusion in the ETAS model. We present predictions and insights provided by the ETAS to CTRW mapping which suggest different ways for studying seismic catalogs. Finally, we discuss the present evidence for our predicted subdiffusion of seismicity triggered by a main shock, stressing the caveats and limitations of previous empirical works.

Journal Article↗
PubMed1982

A random walk model for the migration of Strongylus vulgaris in the intestinal arteries of the horse.

A study of the migration of fourth stage larvae of the parasite Strongylus vulgaris in the intestinal arteries of the horse is presented. It is established, that the larvae migrate along the arteries in almost straight lines. It is suggested that this is primarily due to their ability to sense the curvature of the vessel wall, and not, as might have been expected, because of an ability to sense the direction of blood flow. A larva will sometimes alter its direction of motion when encountering a small off-branching artery. This behaviour suggests, that the migration of S. vulgaris larvae can be modeled as a one-dimensional discrete random walk on a long time scale. This model is simpler than any deterministic model and, in particular, does not require the existence of a predilection site. The available data is not, however, sufficient for a convincing, quantitative test of the model. The proposed reluctance of the larvae to bend into off-branching arteries is used to explain the crowding of larvae in the cranial mesenteric artery.

Animals↗