scholarly journals Migration of individual microvessel endothelial cells: stochastic model and parameter measurement

1991 ◽  
Vol 99 (2) ◽  
pp. 419-430 ◽  
Author(s):  
C.L. Stokes ◽  
D.A. Lauffenburger ◽  
S.K. Williams
Keyword(s):  
Individual Cell ◽  
Mean Square Displacement ◽  
Cell Movement ◽  
Random Motility ◽  
Directional Bias ◽  
Decay Rate Constant ◽  
Persistence Time ◽  
Physiological Processes ◽  
The Mean ◽  
Alpha Beta

Analysis of cell motility effects in physiological processes can be facilitated by a mathematical model capable of simulating individual cell movement paths. A quantitative description of motility of individual cells would be useful, for example, in the study of the formation of new blood vessel networks in angiogenesis by microvessel endothelial cell (MEC) migration. In this paper we propose a stochastic mathematical model for the random motility and chemotaxis of single cells, and evaluate migration paths of MEC in terms of this model. In our model, cell velocity under random motility conditions is described as a persistent random walk using the Ornstein-Uhlenbeck (O-U) process. Two parameters quantify this process: the magnitude of random movement accelerations, alpha, and a decay rate constant for movement velocity, beta. Two other quantities often used in measurements of individual cell random motility properties—cell speed, S, and persistence time in velocity, Pv—can be defined in terms of the fundamental stochastic parameters alpha and beta by: S =square root (alpha/beta) and Pv = 1/beta. We account for chemotactic cell movement in chemoattractant gradients by adding a directional bias term to the O-U process. The magnitude of the directional bias is characterized by the chemotactic responsiveness, kappa. A critical advantage of the proposed model is that it can generate, using experimentally measured values of alpha, beta and kappa, computer simulations of theoretical individual cell paths for use in evaluating the role of cell migration in specific physiological processes. We have used the model to assess MEC migration in the presence of absence of the angiogenic stimulus acidic fibroblast growth factor (aFGF). Time-lapse video was used to observe and track the paths of cells moving in various media, and the mean square displacement was measured from these paths. To test the validity of the model, we compared the mean square displacement measurements of each cell with model predictions of that displacement. The comparison indicates that the O-U process provides a satisfactory description of the random migration at this level of comparison. Using nonlinear regression in these comparisons, we measured the magnitude of random accelerations, alpha, and the velocity decay rate constant, beta, for each cell path. We consequently obtained values for the derived quantities, speed and persistence time. In control medium, we find that alpha = 250 +/− 100 microns 2h-3 and beta = 0.22 +/− 0.03h-1, while in stimulus medium (control plus unpurified aFGF) alpha = 1900 +/− 720 microns 2h-3 and beta = 0.99 +/− 0.37h-1.(ABSTRACT TRUNCATED AT 400 WORDS)

scholarly journals A stochastic model for leukocyte random motility and chemotaxis based on receptor binding fluctuations

1988 ◽  
Vol 106 (2) ◽  
pp. 303-309 ◽  
Author(s):  
RT Tranquillo ◽  
DA Lauffenburger ◽  
SH Zigmond
Keyword(s):  
Random Walk ◽  
Receptor Binding ◽  
Cell Movement ◽  
Movement Behavior ◽  
Random Motility ◽  
Concentration Gradients ◽  
Theoretical Understanding ◽  
Directional Bias ◽  
Persistence Time ◽  
Orientation Bias

Two central features of polymorphonuclear leukocyte chemosensory movement behavior demand fundamental theoretical understanding. In uniform concentrations of chemoattractant, these cells exhibit a persistent random walk, with a characteristic "persistence time" between significant changes in direction. In chemoattractant 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 chemoattractant requires that both the persistence time and the orientation bias be explained within a unifying framework. In this paper, we offer the possibility that "noise" in the cellular signal perception/response mechanism can simultaneously account for these two key phenomena. In particular, we develop a stochastic mathematical model for cell locomotion based on kinetic fluctuations in chemoattractant/receptor binding. This model can simulate cell paths similar to those observed experimentally, under conditions of uniform chemoattractant concentrations as well as chemoattractant concentration gradients. Furthermore, this model can quantitatively predict both cell persistence time and dependence of orientation bias on gradient size. 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.

scholarly journals Alternating regimes of motion in cell motility models

2019 ◽  
Author(s):  
Nara Guisoni ◽  
Karina I. Mazzitello ◽  
Luis Diambra
Keyword(s):  
Anomalous Diffusion ◽  
Mean Square Displacement ◽  
Cell Movement ◽  
Cell Polarization ◽  
Dependent Manner ◽  
Spatial Correlations ◽  
Cellular Potts Model ◽  
Driving Field ◽  
First Case ◽  
The Mean

Cellular movement is a complex dynamic process, resulting from the interaction of multiple elements at the intra and extra-cellular levels. This epiphenomenon presents a variety of behaviors, which can include normal and anomalous diffusion or collective migration. In some cases cells can get neighborhood information through chemical or mechanical cues. A unified understanding about how such information can influence the dynamics of cell movement is still lacking. In order to improve our comprehension of cell migration we consider a cellular Potts model where cells move actively in the direction of a driving field. The intensity of this driving field is constant, while its orientation can evolves according to two alternative dynamics based on the Ornstein-Uhlenbeck process. In the first case, the next orientation of the driving field depends on the previous direction of the field. In the second case, the direction update considers the mean orientation performed by the cell in previous steps. Thus, the latter update rule mimics the ability of cells to perceive the environment, avoiding obstacles and thus increasing the cellular displacement. Our results indicate that both dynamics introduce temporal and spatial correlations in cell velocity in a friction coefficient and cell density dependent manner. Furthermore, we observe alternating regimes in the mean square displacement, with normal and anomalous diffusion. The crossovers between superdiffusive and diffusive regimes, are strongly affected by both the driving field dynamics and cell-cell interactions. In this sense, when cell polarization update grants information about the previous cellular displacement decreases the duration of the diffusive regime, in particular for high density cultures.

Ratio imaging of intracellular ion concentration

1992 ◽  
Vol 50 (2) ◽  
pp. 1160-1161
Author(s):  
Stephen R. Bolsover
Keyword(s):  
Individual Cell ◽  
Video Camera ◽  
Field Of View ◽  
Ion Concentration ◽  
Fluorescence Signal ◽  
Ion Imaging ◽  
Ratiometric Fluorescence ◽  
Ratio Imaging ◽  
The Mean ◽  
The Many

The field of intracellular ion concentration measurement expanded greatly in the 1980's due primarily to the development by Roger Tsien of ratiometric fluorescence dyes. These dyes have many applications, and in particular they make possible to image ion concentrations: to produce maps of the ion concentration within living cells. Ion imagers comprise a fluorescence microscope, an imaging light detector such as a video camera, and a computer system to process the fluorescence signal and display the map of ion concentration.Ion imaging can be used for two distinct purposes. In the first, the imager looks at a field of cells, measuring the mean ion concentration in each cell of the many in the field of view. One can then, for instance, challenge the cells with an agonist and examine the response of each individual cell. Ion imagers are not necessary for this sort of experiment: one can instead use a system that measures the mean ion concentration in a just one cell at any one time. However, they are very much more convenient.

scholarly journals Reconstruction of Diffusion Coefficients and Power Exponents from Single Lagrangian Trajectories

Fluids ◽  
2021 ◽  
Vol 6 (3) ◽  
pp. 111
Author(s):  
Leonid M. Ivanov ◽  
Collins A. Collins ◽  
Tetyana Margolina
Keyword(s):  
Black Sea ◽  
Diffusion Coefficients ◽  
Current System ◽  
Mean Square Displacement ◽  
California Current ◽  
The Black Sea ◽  
Mean Square ◽  
California Current System ◽  
The Mean ◽  
Non Gaussian

Using discrete wavelets, a novel technique is developed to estimate turbulent diffusion coefficients and power exponents from single Lagrangian particle trajectories. The technique differs from the classical approach (Davis (1991)’s technique) because averaging over a statistical ensemble of the mean square displacement (<X2>) is replaced by averaging along a single Lagrangian trajectory X(t) = {X(t), Y(t)}. Metzler et al. (2014) have demonstrated that for an ergodic (for example, normal diffusion) flow, the mean square displacement is <X2> = limT→∞τX2(T,s), where τX2 (T, s) = 1/(T − s) ∫0T−s(X(t+Δt) − X(t))2 dt, T and s are observational and lag times but for weak non-ergodic (such as super-diffusion and sub-diffusion) flows <X2> = limT→∞≪τX2(T,s)≫, where ≪…≫ is some additional averaging. Numerical calculations for surface drifters in the Black Sea and isobaric RAFOS floats deployed at mid depths in the California Current system demonstrated that the reconstructed diffusion coefficients were smaller than those calculated by Davis (1991)’s technique. This difference is caused by the choice of the Lagrangian mean. The technique proposed here is applied to the analysis of Lagrangian motions in the Black Sea (horizontal diffusion coefficients varied from 105 to 106 cm2/s) and for the sub-diffusion of two RAFOS floats in the California Current system where power exponents varied from 0.65 to 0.72. RAFOS float motions were found to be strongly non-ergodic and non-Gaussian.

scholarly journals Subdiffusive Reaction Model of Molecular Species in Liquid Layers: Fractional Reaction-Telegraph Approach

2021 ◽  
Vol 5 (2) ◽  
pp. 51
Author(s):  
Ashraf M. Tawfik ◽  
Mohamed Mokhtar Hefny
Keyword(s):  
Molecular Species ◽  
Transport Model ◽  
Mean Square Displacement ◽  
Telegraph Equation ◽  
Reaction Model ◽  
Simulation Techniques ◽  
Experimental Works ◽  
The Mean ◽  
Classical Transport ◽  
Fractional Reaction

In recent years, different experimental works with molecular simulation techniques have been developed to study the transport of plasma-generated reactive species in liquid layers. Here, we improve the classical transport model that describes the molecular species movement in liquid layers via considering the fractional reaction–telegraph equation. We have considered the fractional equation to describe a non-Brownian motion of molecular species in a liquid layer, which have different diffusivities. The analytical solution of the fractional reaction–telegraph equation, which is defined in terms of the Caputo fractional derivative, is obtained by using the Laplace–Fourier technique. The profiles of species density with the mean square displacement are discussed in each case for different values of the time-fractional order and relaxation time.

Molecular Dynamics Study of Microscopic Mechanism of Diffusion in Li2SiO3 System

1991 ◽  
Vol 46 (7) ◽  
pp. 616-620 ◽  
Author(s):  
Junko Habasaki
Keyword(s):  
Molecular Dynamics ◽  
Coordination Number ◽  
Md Simulation ◽  
Mean Square Displacement ◽  
Mean Square ◽  
Lithium Ions ◽  
Microscopic Mechanism ◽  
Trapping Model ◽  
The Mean

MD simulation has been performed to learn the microscopic mechanism of diffusion of ions in the Li2SiO3 system. The motion of lithium ions can be explained by the trapping model, where lithium is trapped in the polyhedron and moves with fluctuation of the coordination number. The mean square displacement of lithium was found to correlate well with the net changes in coordination number.

THE EFFECT OF PREMELTING: STUDY FOR SEMI-INFINITE CRYSTALS AND NANO-SYSTEMS

1994 ◽  
Vol 08 (24) ◽  
pp. 3411-3422 ◽  
Author(s):  
W. SCHOMMERS
Keyword(s):  
Pair Correlation ◽  
Mean Square Displacement ◽  
Phonon Density ◽  
Mean Square ◽  
Phonon Density Of States ◽  
Molecular Dynamics Calculations ◽  
Theory Of Melting ◽  
The Mean ◽  
Dynamical Properties ◽  
Reliable Interaction

The effect of premelting is of particular interest in connection with the theory of melting. In this paper, we discuss the structural and dynamical properties of the surfaces of semi-infinite crystals as well as of nano-clusters, which show the effect of premelting. The investigations are based on molecular-dynamics calculations: different models are used for the systematic study of the effect of premelting. In particular, the behaviour of the following functions have been studied: pair correlation function, generalized phonon density of states, and the mean-square displacement as a function of time. The calculations have been done for krypton since for this substance a reliable interaction potential is available.

Characterization of Polymer Clay Nanocomposite Electrolyte Motions via Combined NMR and Neutron Scattering Studies

2002 ◽  
Vol 756 ◽  
Author(s):  
Luis J. Smith ◽  
Jean-Marc Zanotti ◽  
Giselle Sandi ◽  
Kathleen A. Carrado ◽  
Patrice Porion ◽  
...  
Keyword(s):  
Neutron Scattering ◽  
Mean Square Displacement ◽  
Polymer Clay Nanocomposite ◽  
Scattering Measurements ◽  
Lower Activation ◽  
Poly Ethylene Oxide ◽  
Nanocomposite Electrolyte ◽  
The Mean ◽  
Poly Ethylene

ABSTRACTThe activation energies for poly(ethylene oxide) motion in a polymer clay composite are reported for the polymer intercalated and external to the clay. PEO intercalated into the clay is found to have a lower activation energy for motion but also a larger Arrhenius prefactor, by almost two orders of magnitude, than for PEO found external to the clay. Neutron scattering measurements confirm the presence of two environments and the effects of confinement on the mean square displacement of the PEO.

Non-Markovian effect of the fractional damping environment and Newton’s second law of motion

2018 ◽  
Vol 32 (19) ◽  
pp. 1850210
Author(s):  
Chun-Yang Wang ◽  
Zhao-Peng Sun ◽  
Ming Qin ◽  
Yu-Qing Xu ◽  
Shu-Qin Lv ◽  
...  
Keyword(s):  
Diffusion Process ◽  
Mean Square Displacement ◽  
Dynamical Analysis ◽  
Second Law ◽  
Mean Square ◽  
Fractional Damping ◽  
Dynamical Mechanism ◽  
Brownian Particles ◽  
The Mean ◽  
Dissipative Environments

We report, in this paper, a recent study on the dynamical mechanism of Brownian particles diffusing in the fractional damping environment, where several important quantities such as the mean square displacement (MSD) and mean square velocity are calculated for dynamical analysis. A particular type of backward motion is found in the diffusion process. The reason of it is analyzed intrinsically by comparing with the diffusion in various dissipative environments. Results show that the diffusion in the fractional damping environment obeys the Langevin dynamics which is quite different form what is expected.

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