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PubMed1984

Analysis of cell movement.

The methods of statistical physics have been applied to the analysis of cell movement. Human leukocytes (granulocytes) were observed using time-lapse photography. The center of gravity of a cell, variations of cell shape, and cell orientation were investigated. This analytical description leads to a better understanding of cell movement. Stationary motion of a cell is described by the anisotropy of the cell shape. The cell displacement can be characterized by three different types of movement: The persistent mode where the cell moves away from an arbitrary chosen origin with its track velocity. The diffusion mode where the cells become dispersed in space by a random walk process. The drift mode where the cell moves with a drift velocity, v parallel, in a concentration gradient of chemoattractant molecules. The chemokinetic response is described by the diffusion constant D (= 240 microns2/min) and the track velocity vc (= 30 microns/min). The chemotactic response is described by the degree of orientation P1 (= 0.8), which is identical with the McCutcheon index and the chemotropism index. Cell movement can be described by elementary moving states, and the life time of such a moving state is 0.5 min. The survival probability of the moving state is determined by an internal program. It is not described by a stochastic process. The angular change in moving direction is also programmed, as the square root of the mean square angular change is +/- 50 degrees. The plus and minus direction are equally probable in a chemokinetic response. However, in a chemotactic assay the plus and minus directions are not equally probably. We found that the information transfer from the chemotactic gradient to the migrating cell is 1 bit per change in moving direction. A disturbance in this information transfer leads to an order-disorder transition. Furthermore, we found that the migrating cell exhibits a directional memory of 75 s.

Biophysical Phenomena↗

PubMed1984

Steady state length distribution of F-actin under controlled fragmentation and mechanism of length redistribution following fragmentation.

Under controlled levels of fragmentation by sonication in the presence of ATP, actin filaments reached different length distributions corresponding to different steady states of polymerization. When the sonication was interrupted, a spontaneous decrease in the number of filaments and corresponding increase in length was observed. The kinetics of the process of length redistribution subsequent to fragmentation was studied for the simpler case of F-actin filaments at equilibrium in the presence of ADP. Analysis of the data shows that a diffusion-like random walk mechanism of length redistribution quantitatively accounts for the observations much better than the previously proposed end-to-end reannealing of filaments. The involvement of this process in the kinetics of actin polymerization and in establishing the length distribution at steady state is discussed.

Actins↗

PubMed1984

Invasion of collagen gels by mouse lymphoid cells.

Small mouse lymphocytes from lymph nodes rapidly invaded three-dimensional collagen gels (in the absence of any added chemical attractant). In short-term assays (2-8 hr) this property was restricted to 20-25% of the cell population. Invasion was an active process involving cell locomotion. Time-lapse cinematography revealed that movement was erratic with frequent changes in cell speed. Tracks of cell paths within collagen gels demonstrated that lymphocytes made narrow angles of turn and thus showed a 'persistent random-walk' similar to other cell types moving on plane substrata. Analysis of lymphocyte movement within aligned collagen gels demonstrated that locomotion was biased in the axis of fibre alignment, i.e. lymphocytes showed contact guidance. Separated B lymphocytes invaded collagen gels at a slower rate than unseparated lymph node cells, as also did T cells purified by filtration through nylon wool columns. This latter anomaly implied that nylon wool filtration selectively depleted cells with invasive characteristics from a heterogeneous lymphocyte population. A comparison of Peyer's patch and lymph node lymphocytes showed that both populations invaded at the same rate but the latter cell type did this in greater numbers. This difference may reflect the different proportions of B and T lymphocytes in the two tissues. Lymphocytes from oxazolone-stimulated lymph nodes showed greatly increased movement into collagen matrices compared to unstimulated control lymph node lymphocytes. This increase was demonstrated to be a property of the blast cell population by separating the cells on Percoll gradients into lymphoblast-enriched and -depleted populations.

Animals↗

PubMed1983

Early stopping for sequential restricted tests of binomial distributions.

In applications of restricted sequential procedures, the accumulating data can provide a strong indication that rejection of the null hypothesis is very unlikely if sampling is continued; however, trial termination with acceptance of the null hypothesis can require a large number of additional observations. Modifications of restricted sequential plans, based on the conditional probability of an inference contrary to that suggested by the data, are presented for trials with binary responses. The derived tests provide the potential for early stopping with acceptance of the null hypothesis and reduction of the expected stopping times. Properties of the stopping-time distributions are obtained exactly by considering the absorption probabilities of a binomial random walk on the lattice determined by the restricted sequential design. Relative efficiencies of the derived tests to the corresponding sequential probability ratio tests are presented, along with an example based on data from a clinical trial.

Statistics as Topic↗

PubMed1984

The response of human neutrophils to a chemotactic tripeptide (N-formyl-methionyl-leucyl-phenylalanine) studied by microcinematography.

A quantitative microcinematographic technique for the measurement of cellular motion in response to chemical influences is described. The data are analyzed by using a magnetic digitizer connected to a computer, permitting comparison of several characteristics of such motion. When human granulocytes are placed in a gradient of formyl-methionyl-leucyl-phenylalanine (fMLP) (concentration 10(-6)-10(-8) mol/L) against buffer, the motion of the cells is increased in velocity (chemokinesis) and is directed toward the chemoattractant, as measured by the orientation of the vector of motion. This directionality is confirmed by positive values for the McCutcheon index and analysis of directed linear displacement. Concentrations of fMLP below 10(-9) mol/L did not result in chemokinesis or chemotaxis, presumably due to insufficient stimulus. Concentrations of 10(-6) mol/L fMLP and greater resulted in marked stimulation of the cell surface but reduced directionality and velocity of motion compared with cells in a more optimal gradient. Motion of the unstimulated cells tended to be ortholinear , and this was not increased by the presence of a gradient of fMLP. Hence, as previously shown, the Random Walk analysis, which does not give weight to the direction of motion, is not useful in the analysis of the response of these cells to a chemotaxin in this system.

Cell Movement↗

PubMed1982

Comparing multivariate and univariate subject-specific reference regions for blood constituents in healthy persons.

We examined the comparative behavior of subject-specific multivariate and univariate reference regions, using both computer-generated data and serial (semi-annual) measurements of selected analytes in subjects from a large health-maintenance program. Univariate studies under both homeostatic and random-walk time-series models were helpful in defining expected results, but only the homeostatic model was used in multivariate as well as univariate forms. Analysis of the computer-generated data and the real biochemical series produced similar findings, which showed the multivariate subject-specific reference region to be much more conservative than corresponding univariate intervals. That is, a multidimensional point of p correlated observations is quite likely to lie within the individual's multivariate reference region (based on past observation vectors), even when one or more of the observations lie outside their separate reference intervals for that individual. One consequence of this high specificity against univariate false positives in a large surveillance program is a higher than expected proportion of positive multivariate vectors in which none of the values lie outside their univariate ranges. Thus, although the development of multivariate reference regions should be encouraged, they should be used in conjunction with, not instead of, univariate ranges.

Analysis of Variance↗

PubMed1980

The computer leucocyte. Analysis of the random movement of leucocytes in a visual field by means of computer simulation.

In vital preparations moving polymorphonuclear leucocytes (PMNs) disappear from the visual field. The present study provides evidence by means of geometrical analysis and computer simulation, that this disappearance is due to a heterogeneous distribution of the PMNs at the beginning of observation. The path of random-moving computer leucocytes is more tortuous than the path of comparable vital PMNs without obvious attractant, i.e. vital PMNs supposed to be random-moving. This finding is in agreement with the Allan-Wilkinson observation of 'persistent random walk' of vital cells.

Cell Movement↗

PubMed1978

How paradise fish (Macropodus opercularis, L.) explores a chessboard.

We investigated the exploratory movements of Anabantid fishes in a chessboard-like aquarium (divided into 25 communicating compartments) as a new environment. The analysis was based on the observation of the route of two inbred strains of paradise fish (Macropodus opercularis; Teleostei, Anabantoidae). We recorded their movement within the blocks until 100 steps, and compared the obtained process with hypothetical random walks. It turns out within the same period of time the fish meets significantly more new compartments than in the simulated process. The discrepancy between the two processes can be interpreted as the result of a successful exploratory strategy of the fish. In this exploratory movement the fish prefers the outer compartments to the inner ones, a fact that explains the striking difference between the actual behaviour and the "uniform simulation". This is obviously so, since the empirical data show that the transition probabilities from the actual compartment to the possible neighbouring compartments differ greatly. However, a model taking this inhomogeneity into account still does not fit sufficiently, indicating that this exploratory strategy is more complicated than our memoryless construction. Moreover, there are differences between the two strains investigated, which might reflect some role of genetic factors.

Animals↗

PubMed1994

The regulation of endothelial cell motility by p21 ras.

Directed endothelial cell (EC) movement is required for the development and repair of blood vessels and plays a critical role in angiogenic processes obligatory for large tumor formation. We now report that ras proteins have a critical role in regulation of movement of normal mammalian cells. Bovine aortic EC microinjected with oncogenic Ha-ras enter further into an artificial wound than uninjected cells. Treatment with oncogenic Ha-ras also converts the cell paths from nearly linear in control cells to apparent 'random-walk' trajectories in treated cells, suggesting that oncogenic ras alters the normal control processes regulating cell motility. Botulinum toxin C blocks ras-stimulated motility indicating that a member of the p21 rho family is a downstream participant in the motile pathway. In related experiments we have observed that microinjection of the neutralizing, ras-specific, Y13-259 monoclonal antibody completely blocks both basal and basic fibroblast growth factor-stimulated movement of aortic EC. Y13-259 blocks the initiation of EC movement, as well as the continued progress of cells already in motion, suggesting that ras activity is continuously required throughout the motile process. Together these data indicate that ras is an integral component of the signaling pathway regulating cell movement.

Animals↗

PubMed1994

Apolipoprotein B synthesis: a square lattice model.

We have formulated a random walk model for emerging apolipoprotein B interaction with its translocation channel on the surface of the rough endoplasmic reticulum based on the assumption that this interaction is a diffusion-mediated process. From this model, we found that a substantial proportion of mRNA-ribosome complexes was not bound to their translocation channels at any given moment of quasi-steady state. The duration of polypeptide chain elongation was an important determinant of the number of mRNA-ribosome complexes bound to their channels, but it had little net effect on the integrated rate of protein synthesis and translocation. The rates of protein synthesis and translocation for different secretory proteins that were cotranslationally translocated were very similar provided that they had similar mRNA concentration. We conclude that one of the control mechanisms regulating apolipoprotein B production may rely on the properties of translocation channels to determine the fate of newly synthesized apolipoprotein B molecules.

Animals↗

PubMed1996

Influence of conformational flexibility of their active sites on the electronic conductivity of enzymes.

The a.c. conductivity of the proteins lysozyme and subtilisin, both in their active and inactive or inhibited forms were determined theoretically. For this, quantum mechanical calculations and a random walk theory were used. The conclusions are that these enzymatic proteins can easily transport electrons which is most probably important in their role as catalysators of biochemical reactions. The electron transport is sensitive to three-dimensional changes of the active sites of these enzymes which have more flexibility than the whole molecule. Therefore, the flexibility of the active sites of enzyme catalysts is not only important for the conformational fitting with the reactants, but also strongly influences the transport in biochemical reactions.

Binding Sites↗

PubMed1997

[Units of DNA replication in S-phase human cells].

Current methods of physical mapping allow the estimation of genomic distances (i.e. DNA contents) from linear distances between DNA markers in interphase nuclei, and in this study we estimated the size of focal centers of DNA replication in cultured S-phase human cells. Our results indicate that the conformation of S-phase chromosome fibres in the range of contour lengths 0.1-3.0 microns fits the random walk model and, therefore, the quantitative methods of interphase mapping can be applied to the estimation of sizes of replication units. The obtained data show the existence of multiple non-clustered small units less than 150 kb in size, equivalent to small replicons detected by fiber DNA radioautography, and also a significant fraction of big units more than 500 kb in size, representing groups of small replicons and/or big replicons. These big units are detected as chains of small replication foci, probably reflecting the structural chromatin organization in well-known loop domains, since the experimentally induced decrease of replicons to the average size 12 kb does not lead to any change in the pattern of indicated chains.

Adenocarcinoma↗

PubMed1997

A dynamic frailty model for multivariate survival data.

We consider the statistical modeling of data consisting of many study subjects with serially correlated multivariate survival responses. The (ordinary) frailty model handles the serial correlation in such data by introducing an unobserved multiplicative random effect term, called the frailty, in the hazard function. The frailties are often assumed to be identical for the survival times from the same unit. We have generalized the frailty model by allowing the frailties to vary stochastically with the indices. We have proposed a simple scheme to update the dynamic frailties. This approach assumes that the random effects are gamma distributed. At each occurrence, the two gamma parameters are updated according to the past information. In terms of their marginal distributions, the dynamic frailties form a multiplicative random walk. This approach results in a tractable likelihood. The small sample behavior of the MLE is studied via a simulation experiment. The model is then illustrated with a data set from an animal carcinogenesis experiment.

Biometry↗

PubMed1998

Gaussian-chain model for the formation of chromosome aberrations.

In this report a model is developed for the formation of chromosome aberrations by approximating interphase chromosomes as random-walk Gaussian chains. The following results support the model: (1) The ratio of dicentrics to centric rings (F) was calculated for the case of equal-sized metacentric chromosomes in a spherical nucleus: F = 4-23, which agrees well with the experimental range of 5-20 reported in the literature for human lymphocytes. (2) The prediction of the model that the probabilities for intrachromosomal and interchromosomal exchanges are inversely proportional to nuclear volume agrees well with data for chromosome exchanges in lymphocytes compared to normal fibroblasts, and with data for survival of plateau-phase Chinese hamster V79 cells after postirradiation treatment with hypertonic salt solutions. (3) The prediction of the model that the probability of interchromosomal exchanges is greater in spherical nuclei than in flat nuclei agrees with experimental data for differences in survival of human fibroblasts (ataxia telangiectasia and normal) irradiated as monolayers and plated immediately or several hours (delayed plating) after irradiation.

Animals↗

PubMed1998

Denatured states of yeast phosphoglycerate kinase.

Structures of proteins in unfolded states have important implications for the protein folding problem and for the translocation of polypeptide chains. Acid-denatured, cold-denatured, and 6 M guanidine hydrochloride (GuHCl) denatured yeast phosphoglycerate kinase (PGK) are ensembles of flexible unfolded molecules with rapidly interconverting structures of the individual polypeptide chains. They differ, however, in their physical properties, such as in coil size and in stiffness over a short distance along the chain. These properties of polypeptide chains can be described well by persistence statistics. A solution containing 0.7 M GuHCl at 4.5 degrees C is nearly a Theta-solvent for PGK. By contrast, 6 M GuHCl is a good solvent for PGK. Acid-denatured PGK at low ionic strength has the most expanded and stiffest chains. The conformation of heat-denatured PGK should be more compact than that of random walk chains at the Theta-point, as can be inferred from measurements on other proteins. Investigations of heat-denatured PGK by scattering methods are unfeasible due to aggregation of the protein. The persistence length as a measure of chain stiffness varies between a = 1.74 nm for cold-denatured PGK and a = 3.0 nm for acid-denatured PGK. The distribution functions of the gyration radii were calculated from the X-ray scattering data for all unfolded states and compared with the radius of gyration of the natively folded molecule.

Models, Molecular↗

PubMed1998

A nonparametric approach to a survival study with surrogate endpoints.

A nonparametric estimator for the joint distribution of a survival time and surrogate response time, which may occur earlier during follow-up, is presented. In the absence of the surrogate response variable, the estimator reduces to the Kaplan Meier nonparametric estimator for the survival time alone. The estimator derived in this paper is done so in a particular novel way using an exchangeable process (reinforced random walks) to model individual observations. The methodology introduced in the paper is readily extended to modelling multiple state processes.

Humans↗

PubMed1998

A statistical paradigm for neural spike train decoding applied to position prediction from ensemble firing patterns of rat hippocampal place cells.

The problem of predicting the position of a freely foraging rat based on the ensemble firing patterns of place cells recorded from the CA1 region of its hippocampus is used to develop a two-stage statistical paradigm for neural spike train decoding. In the first, or encoding stage, place cell spiking activity is modeled as an inhomogeneous Poisson process whose instantaneous rate is a function of the animal's position in space and phase of its theta rhythm. The animal's path is modeled as a Gaussian random walk. In the second, or decoding stage, a Bayesian statistical paradigm is used to derive a nonlinear recursive causal filter algorithm for predicting the position of the animal from the place cell ensemble firing patterns. The algebra of the decoding algorithm defines an explicit map of the discrete spike trains into the position prediction. The confidence regions for the position predictions quantify spike train information in terms of the most probable locations of the animal given the ensemble firing pattern. Under our inhomogeneous Poisson model position was a three to five times stronger modulator of the place cell spiking activity than theta phase in an open circular environment. For animal 1 (2) the median decoding error based on 34 (33) place cells recorded during 10 min of foraging was 8.0 (7.7) cm. Our statistical paradigm provides a reliable approach for quantifying the spatial information in the ensemble place cell firing patterns and defines a generally applicable framework for studying information encoding in neural systems.

Action Potentials↗

PubMed1998

Supramolecular receptor structures in the plasma membrane of lymphocytes revealed by flow cytometric energy transfer, scanning force- and transmission electron-microscopic analyses.

Receptors in the plasma membrane of blood cells in general and in that of lymphocytes in particular are supposed to move around in a random walk fashion relatively freely driven by thermal diffusion, as described by the Singer-Nicolson fluid mosaic membrane model. In this article we summarized data and techniques that indicated nonrandom codistribution patterns of receptor superstructures under conditions, where the generation of such molecular colocalizations by the methods themselves were excluded. Application of fluorescence energy transfer in a flow cytometer helped to analyze such codistribution patterns in cell populations. After normalizing energy transfer values for possible differences between labeling ratios of the targeting monoclonal antibodies and using the mean values of energy transfer distribution curves, two-dimensional receptor maps were generated from data obtained in a pair-wise fashion between receptors. Major histocompatibility complex (MHC) class I and II, intercellular adhesion molecule-1 (ICAM-1), TcR-CD3-CD4, tetraspan molecules (CD81, CD82, CD53), and the subunits of the multisubunit IL-2 receptor displayed nonrandom codistribution patterns sometimes with, but very frequently without induction by their ligand. Immunogold-bead "sandwich" labeling analyzed by atomic force microscopy has shown that such receptor "islands" existed also in "receptor-island-groups". This indicated the existence of nonrandom receptor distribution of MHC class I and II molecules also at an elevated hierarchical level. An analysis is given herein concerning a standardized approach. The apparent incompatibility of these supramolecular patterns with the Singer-Nicolson type "free-protein and lipid-mobility paradigm" was resolved by recommending an additional emphasis on the mosaicism of the membrane besides receptor mobility.

Antibodies, Monoclonal↗