scholarly journals Random Walks of a Cell With Correlated Speed and Persistence Influenced by the Extracellular Topography

2021 ◽  
Vol 9 ◽  
Author(s):  
Kejie Chen ◽  
Kai-Rong Qin
Keyword(s):  
Cell Migration ◽  
Random Walk ◽  
Cell Types ◽  
Coarse Grained ◽  
Search Efficiency ◽  
Complex Environments ◽  
Unit Distance ◽  
Lévy Walk ◽  
Levy Walk ◽  
A Cell

Cell migration through extracellular matrices is critical to many physiological processes, such as tissue development, immunological response and cancer metastasis. Previous models including persistent random walk (PRW) and Lévy walk only explain the migratory dynamics of some cell types in a homogeneous environment. Recently, it was discovered that the intracellular actin flow can robustly ensure a universal coupling between cell migratory speed and persistence for a variety of cell types migrating in the in vitro assays and live tissues. However, effects of the correlation between speed and persistence on the macroscopic cell migration dynamics and patterns in complex environments are largely unknown. In this study, we developed a Monte Carlo random walk simulation to investigate the motility, the search ability and the search efficiency of a cell moving in both homogeneous and porous environments. The cell is simplified as a dimensionless particle, moving according to PRW, Lévy walk, random walk with linear speed-persistence correlation (linear RWSP) and random walk with nonlinear speed-persistence correlation (nonlinear RWSP). The coarse-grained analysis showed that the nonlinear RWSP achieved the largest motility in both homogeneous and porous environments. When a particle searches for targets, the nonlinear coupling of speed and persistence improves the search ability (i.e. find more targets in a fixed time period), but sacrifices the search efficiency (i.e. find less targets per unit distance). Moreover, both the convex and concave pores restrict particle motion, especially for the nonlinear RWSP and Lévy walk. Overall, our results demonstrate that the nonlinear correlation of speed and persistence has the potential to enhance the motility and searching properties in complex environments, and could serve as a starting point for more detailed studies of active particles in biological, engineering and social science fields.

scholarly journals Differentiating the Lévy walk from a composite correlated random walk

2015 ◽  
Vol 6 (10) ◽  
pp. 1179-1189 ◽  
Author(s):  
Marie Auger‐Méthé ◽  
Andrew E. Derocher ◽  
Michael J. Plank ◽  
Edward A. Codling ◽  
Mark A. Lewis
Keyword(s):  
Random Walk ◽  
Correlated Random Walk ◽  
Lévy Walk ◽  
Levy Walk

scholarly journals Swimming Escherichia coli explore the environment by Lévy walk

2021 ◽  
Author(s):  
Haiyan Huo ◽  
Rui He ◽  
Rongjing Zhang ◽  
Junhua Yuan
Keyword(s):  
Random Walk ◽  
Response Regulator ◽  
Bacterial Chemotaxis ◽  
Random Fluctuation ◽  
Aqueous Environment ◽  
E Coli ◽  
Lévy Walk ◽  
Diffusion Characteristics ◽  
Levy Walk ◽  
Run Lengths

E. coli cells swim in aqueous environment in a random walk of alternating runs and tumbles. The diffusion characteristics of this random walk remains unclear. Here, by tracking the swimming of wildtype cells in a 3d homogeneous environment, we found that their trajectories are super diffusive, consistent with Lévy walk behavior. For comparison, we tracked the swimming of mutant cells that lack the chemotaxis signaling noise (the steady-state fluctuation of the concentration of the chemotaxis response regulator CheY-P), and found that their trajectories are normal diffusive. Therefore, wildtype E. coli cells explore the environment by Lévy walk, which originates from the chemotaxis signaling noise. This Lévy walk pattern enhances their efficiency in environmental exploration. Importance E. coli cells explore the environment in a random walk of alternating runs and tumbles. By tracking the 3d trajectories of E. coli cells in aqueous environment, we find that their trajectories are super diffusive, with a power-law shape for the distribution of run lengths, which is characteristics of Lévy walk. We further show that this Lévy walk behavior is due to the random fluctuation of the output level of the bacterial chemotaxis pathway, and it enhances the efficiency of the bacteria in exploring the environment.

scholarly journals Mechanical Interactions between a Cell and an Extracellular Environment Facilitate Durotactic Cell Migration

2018 ◽  
Author(s):  
Abdel-Rahman Hassan ◽  
Thomas Biel ◽  
Taeyoon Kim
Keyword(s):  
Cell Migration ◽  
Computational Models ◽  
Biomechanical Model ◽  
Coarse Grained ◽  
Physiological Processes ◽  
Specific Direction ◽  
A Cell ◽  
Stiffness Profile ◽  
Contractile Forces ◽  
Extracellular Environment

ABSTRACTCell migration is a fundamental process in biological systems, playing an important role for diverse physiological processes. Cells often exhibit directed migration in a specific direction in response to various types of cues. In particular, cells are able to sense the rigidity of surrounding environments and then migrate towards stiffer regions. To understand this mechanosensitive behavior called durotaxis, several computational models have been developed. However, most of the models made phenomenological assumptions to recapitulate durotactic behaviors, significantly limiting insights provided from these studies. In this study, we developed a computational biomechanical model without any phenomenological assumption to illuminate intrinsic mechanisms of durotactic behaviors of cells migrating on a two-dimensional substrate. The model consists of a simplified cell generating contractile forces and a deformable substrate coarse-grained into an irregular triangulated mesh. Using the model, we demonstrated that durotactic behaviors emerge from purely mechanical interactions between the cell and the underlying substrate. We investigated how durotactic migration is regulated by biophysical properties of the substrate, including elasticity, viscosity, and stiffness profile.

scholarly journals Cell migration in complex environments: chemotaxis and topographical obstacles

2020 ◽  
Vol 67 ◽  
pp. 191-209 ◽  
Author(s):  
Alessandro Cucchi ◽  
Christèle Etchegaray ◽  
Nicolas Meunier ◽  
Laurent Navoret ◽  
Lamis Sabbagh
Keyword(s):  
Cell Migration ◽  
Threshold Value ◽  
External Signal ◽  
Complex Environments ◽  
Cell Dynamics ◽  
Contact Algorithm ◽  
A Cell ◽  
And Migration ◽  
The Impact ◽  
Force Intensity

Cell migration is a complex phenomenon that plays an important role in many biological processes. Our aim here is to build and study models of reduced complexity to describe some aspects of cell motility in tissues. Precisely, we study the impact of some biochemical and mechanical cues on the cell dynamics in a 2D framework. For that purpose, we model the cell as an active particle with a velocity solution to a particular Stochastic Differential Equation that describes the intracellular dynamics as well as the presence of some biochemical cues. In the 1D case, an asymptotic analysis puts to light a transition between migration dominated by the cell’s internal activity and migration dominated by an external signal. In a second step, we use the contact algorithm introduced in [15,18] to describe the cell dynamics in an environment with obstacles. In the 2D case, we study how a cell submitted to a constant directional force that mimics the action of chemoattractant, behaves in the presence of obstacles. We numerically observe the existence of a velocity value that the cell can not exceed even if the directional force intensity increases. We find that this threshold value depends on the number of obstacles. Our result confirms a result that was already observed in a discrete framework in [3,4].

scholarly journals Reduction of a stochastic model of gene expression: Lagrangian dynamics gives access to basins of attraction as cell types and metastabilty

2020 ◽  
Author(s):  
Elias Ventre ◽  
Thibault Espinasse ◽  
Charles-Edouard Bréhier ◽  
Vincent Calvez ◽  
Thomas Lepoutre ◽  
...  
Keyword(s):  
Gene Expression ◽  
Stochastic Model ◽  
Cell Types ◽  
Basins Of Attraction ◽  
Coarse Grained ◽  
Model Parameters ◽  
Toggle Switch ◽  
Lagrangian Dynamics ◽  
Coarse Grained Model ◽  
A Cell

AbstractDifferentiation is the process whereby a cell acquires a specific phenotype, by differential gene expression as a function of time. This is thought to result from the dynamical functioning of an underlying Gene Regulatory Network (GRN). The precise path from the stochastic GRN behavior to the resulting cell state is still an open question. In this work we propose to reduce a stochastic model of gene expression, where a cell is represented by a vector in a continuous space of gene expression, to a discrete coarse-grained model on a limited number of cell types. We develop analytical results and numerical tools to perform this reduction for a specific model characterizing the evolution of a cell by a system of piecewise deterministic Markov processes (PDMP). Solving a spectral problem, we find the explicit variational form of the rate function associated to a Large deviations principle, for any number of genes. The resulting Lagrangian dynamics allows us to define a deterministic limit, the basins of attraction of which can be identified to cellular types. In this context the quasipotential, describing the transitions between these basins in the weak noise limit, can be defined as the unique solution of an Hamilton-Jacobi equation under a particular constraint. We develop a numerical method for approximating the coarse-grained model parameters, and show its accuracy for a symmetric toggle-switch network. We deduce from the reduced model an analytical approximation of the stationary distribution of the PDMP system, which appears as a beta mixture. Altogether those results establish a rigorous frame for connecting GRN behavior to the resulting cellular behavior, including the calculation of the probability of jumps between cell types.

Cell-extracellular matrix dynamics

2021 ◽  
Author(s):  
Andrew Doyle ◽  
Shayan Nazari ◽  
Kenneth M Yamada
Keyword(s):  
Extracellular Matrix ◽  
Cell Migration ◽  
Cell Types ◽  
Tissue Level ◽  
Matrix Proteins ◽  
Immune Functions ◽  
Integrin Receptors ◽  
Invasion And Metastasis ◽  
Disease States ◽  
A Cell

Abstract The sites of interaction between a cell and its surrounding microenvironment serve as dynamic signaling hubs that regulate cellular adaptations during developmental processes, immune functions, wound healing, cell migration, cancer invasion and metastasis, as well as in many other disease states. For most cell types, these interactions are established by integrin receptors binding directly to extracellular matrix proteins, such as the numerous collagens or fibronectin. For the cell, these points of contact provide vital cues by sampling environmental conditions, both chemical and physical. The overall regulation of this dynamic interaction involves both extracellular and intracellular components and can be highly variable. In this review, we highlight recent advances and hypotheses about the mechanisms and regulation of cell-ECM interactions, from the molecular to the tissue level, with a particular focus on cell migration. We then explore how cancer cell invasion and metastasis are deeply rooted in altered regulation of this vital interaction.

scholarly journals Intermittent inverse-square Lévy walks are optimal for finding targets of all sizes

2021 ◽  
Vol 7 (15) ◽  
pp. eabe8211
Author(s):  
Brieuc Guinard ◽  
Amos Korman
Keyword(s):  
Random Walk ◽  
Mathematical Proof ◽  
Higher Dimensions ◽  
Two Dimensional ◽  
Power Law Distribution ◽  
Arbitrary Size ◽  
Lévy Walk ◽  
Lévy Walks ◽  
Levy Walk ◽  
Biological Organisms

Lévy walks are random walk processes whose step lengths follow a long-tailed power-law distribution. Because of their abundance as movement patterns of biological organisms, substantial theoretical efforts have been devoted to identifying the foraging circumstances that would make such patterns advantageous. However, despite extensive research, there is currently no mathematical proof indicating that Lévy walks are, in any manner, preferable strategies in higher dimensions than one. Here, we prove that in finite two-dimensional terrains, the inverse-square Lévy walk strategy is extremely efficient at finding sparse targets of arbitrary size and shape. Moreover, this holds even under the weak model of intermittent detection. Conversely, any other intermittent Lévy walk fails to efficiently find either large targets or small ones. Our results shed new light on the Lévy foraging hypothesis and are thus expected to affect future experiments on animals performing Lévy walks.

Dendritic cells of the human epidermis: immuno-electron microscopic studies of la antigen reactivity

1978 ◽  
Vol 36 (2) ◽  
pp. 644-645
Author(s):  
G. Rowden ◽  
M. G. Lewis ◽  
T. M. Phillips
Keyword(s):  
Dendritic Cells ◽  
Langerhans Cells ◽  
Cell Types ◽  
Cell Type ◽  
Electron Microscopic ◽  
La Antigen ◽  
Microscopic Studies ◽  
A Cell ◽  
C3 Receptors ◽  
Antigen Reactivity

Langerhans cells of mammalian stratified squamous epithelial have proven to be an enigma since their discovery in 1868. These dendritic suprabasal cells have been considered as related to melanocytes either as effete cells, or as post divisional products. Although grafting experiments seemed to demonstrate the independence of the cell types, much confusion still exists. The presence in the epidermis of a cell type with morphological features seemingly shared by melanocytes and Langerhans cells has been especially troublesome. This so called "indeterminate", or " -dendritic cell" lacks both Langerhans cells granules and melanosomes, yet it is clearly not a keratinocyte. Suggestions have been made that it is related to either Langerhans cells or melanocyte. Recent studies have unequivocally demonstrated that Langerhans cells are independent cells with immune function. They display Fc and C3 receptors on their surface as well as la (immune region associated) antigens.

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