scholarly journals Modelling cell motility and chemotaxis with evolving surface finite elements

2012 ◽  
Vol 9 (76) ◽  
pp. 3027-3044 ◽  
Author(s):  
Charles M. Elliott ◽  
Björn Stinner ◽  
Chandrasekhar Venkataraman
Keyword(s):  
Cell Membrane ◽  
Cell Motility ◽  
Reaction Diffusion ◽  
Cell Polarization ◽  
Computational Method ◽  
Three Dimensions ◽  
Modelling Framework ◽  
Surface Finite Elements ◽  
Evolving Surface ◽  
External Forces

We present a mathematical and a computational framework for the modelling of cell motility. The cell membrane is represented by an evolving surface, with the movement of the cell determined by the interaction of various forces that act normal to the surface. We consider external forces such as those that may arise owing to inhomogeneities in the medium and a pressure that constrains the enclosed volume, as well as internal forces that arise from the reaction of the cells' surface to stretching and bending. We also consider a protrusive force associated with a reaction–diffusion system (RDS) posed on the cell membrane, with cell polarization modelled by this surface RDS. The computational method is based on an evolving surface finite-element method. The general method can account for the large deformations that arise in cell motility and allows the simulation of cell migration in three dimensions. We illustrate applications of the proposed modelling framework and numerical method by reporting on numerical simulations of a model for eukaryotic chemotaxis and a model for the persistent movement of keratocytes in two and three space dimensions. Movies of the simulated cells can be obtained from http://homepages.warwick.ac.uk/∼maskae/CV_Warwick/Chemotaxis.html .

Modeling the Mechanics of Tethers Pulled From the Cochlear Outer Hair Cell Membrane

2008 ◽  
Vol 130 (3) ◽  
Author(s):  
Kristopher R. Schumacher ◽  
Aleksander S. Popel ◽  
Bahman Anvari ◽  
William E. Brownell ◽  
Alexander A. Spector
Keyword(s):  
Cell Membrane ◽  
Hair Cell ◽  
Outer Hair Cell ◽  
Lateral Wall ◽  
Outer Hair Cells ◽  
The Body ◽  
Computational Method ◽  
Membrane Properties ◽  
Bending Modulus ◽  
Sound Amplification

Cell membrane tethers are formed naturally (e.g., in leukocyte rolling) and experimentally to probe membrane properties. In cochlear outer hair cells, the plasma membrane is part of the trilayer lateral wall, where the membrane is attached to the cytoskeleton by a system of radial pillars. The mechanics of these cells is important to the sound amplification and frequency selectivity of the ear. We present a modeling study to simulate the membrane deflection, bending, and interaction with the cytoskeleton in the outer hair cell tether pulling experiment. In our analysis, three regions of the membrane are considered: the body of a cylindrical tether, the area where the membrane is attached and interacts with the cytoskeleton, and the transition region between the two. By using a computational method, we found the shape of the membrane in all three regions over a range of tether lengths and forces observed in experiments. We also analyze the effects of biophysical properties of the membrane, including the bending modulus and the forces of the membrane adhesion to the cytoskeleton. The model’s results provide a better understanding of the mechanics of tethers pulled from cell membranes.

A DNA Molecular Robot Autonomously Walking on the Cell Membrane to Drive the Cell Motility

2021 ◽  
Author(s):  
Hao Li ◽  
Jing Gao ◽  
Lei Cao ◽  
Xuan Xie ◽  
Jiahui Fan ◽  
...  
Keyword(s):  
Cell Membrane ◽  
Cell Motility

A DNA Molecular Robot Autonomously Walking on the Cell Membrane to Drive the Cell Motility

2021 ◽  
Author(s):  
Hao Li ◽  
Jing Gao ◽  
Lei Cao ◽  
Xuan Xie ◽  
Jiahui Fan ◽  
...  
Keyword(s):  
Cell Membrane ◽  
Cell Motility

Leukosialin (CD43, sialophorin) redistribution in uropods of polarized neutrophils is induced by CD43 cross-linking by antibodies, by colchicine or by chemotactic peptides

1997 ◽  
Vol 110 (13) ◽  
pp. 1465-1475
Author(s):  
S. Seveau ◽  
S. Lopez ◽  
P. Lesavre ◽  
J. Guichard ◽  
E.M. Cramer ◽  
...  
Keyword(s):  
Electron Microscopy ◽  
Cell Motility ◽  
Small Proportion ◽  
Cytochalasin B ◽  
Cell Polarization ◽  
Cross Linking ◽  
Chemotactic Peptides ◽  
Butanedione Monoxime ◽  
Major Surface ◽  
Triton X

We investigated a possible association of leukosialin (CD43), the major surface sialoglycoprotein of leukocytes, with neutrophil cytoskeleton. We first analysed the solubility of CD43 in Triton X-100 and observed that CD43 of resting neutrophils was mostly soluble. The small proportion of CD43 molecules, which ‘spontaneously’ precipitated in Triton, appeared associated with F-actin, as demonstrated by the fact that this insolubility did not occur when cells were incubated with cytochalasin B or when F-actin was depolymerized with DNase I in the Triton precipitate. Cell stimulation with anti-CD43 mAb (MEM59) enhanced this CD43-cytoskeleton association. By immunofluorescence as well as by electron microscopy, we observed a redistribution of CD43 on the neutrophil membrane, initially in patches followed by caps, during anti-CD43 cross-linking at 37 degrees C. This capping did not occur at 4 degrees C and was inhibited by cytochalasin B and by a myosin disrupting drug butanedione monoxime, thus providing evidence that the actomyosin contracile sytem is involved in the capping and further suggesting an association of CD43 with the cytoskeleton. Some of the capped cells exhibited a front-tail polarization with CD43 caps located in the uropod at the rear of the cell. Surprisingly, colchicine and the chemotactic factor fNLPNTL which induce neutrophil polarization associated with cell motility, also resulted in a clustering of CD43 in the uropod, independently of a cross-linking of the molecule by mAbs. An intracellular redistribution of F-actin, mainly at the leading front and of myosin in the tail, was observed during CD43 clustering induced by colchicine and in cells polarized by anti-CD43 mAbs cross-linking. We conclude that neutrophil CD43 interacts with the cytoskeleton, either directly or indirectly, to redistribute in the cell uropod under antibodies stimulation or during cell polarization by colchicine, thus highly suggesting that CD43 may be involved in cell polarization.

scholarly journals In silico mechanobiochemical modeling of morphogenesis in cell monolayers

2017 ◽  
Author(s):  
Bahador Marzban ◽  
Xiao Ma ◽  
Xiaoliang Qing ◽  
Hongyan Yuan
Keyword(s):  
Computational Model ◽  
Reaction Diffusion ◽  
Cell Interaction ◽  
Cell Polarization ◽  
Cell Morphogenesis ◽  
Cell Monolayers ◽  
Irregular Shapes ◽  
Cell Substrate ◽  
Living Tissues

Cell morphogenesis is a fundamental process involved in tissue formation. One of the challenges in the fabrication of living tissues in vitro is to recapitulate the complex morphologies of individual cells. Despite tremendous progress in understanding biophysical principles underlying tissue/organ morphogenesis at the organ level, little work has been done to understand morphogenesis at the cellular and microtissue level. In this work, we developed a 2D computational model for studying cell morphogenesis in monolayer tissues. The model is mainly composed of four modules: mechanics of cytoskeleton, cell motility, cell-substrate interaction, and cell-cell interaction. The model integrates the biochemical and mechanical activities within individual cells spatiotemporally. Finite element method (FEM) is used to model the irregular shapes of cells and to solve the resulting system of reaction-diffusion-stress equations. Automated mesh generation is used to handle the element distortion in FEM due to the large shape changes of the cells. The computer program can simulate tens to hundreds of cells interacting with each other and with the elastic substrate on desktop workstations efficiently. The simulations demonstrated that our computational model can be used to study cell polarization, single cell migration, durotaxis, and morphogenesis in cell monolayers.

Cell membrane ? Cytomatrix interactions in cell motility

1990 ◽  
Vol 14 ◽  
pp. 38
Author(s):  
M DEBRABANDER ◽  
R NUYDENS ◽  
H GEERTS ◽  
R NUYENS ◽  
J LEUNISSEN ◽  
...  
Keyword(s):  
Cell Membrane ◽  
Cell Motility

Radiolaria: validating the Turing theory

2017 ◽  
Author(s):  
Bernard Richards
Keyword(s):  
Diffusion Mechanism ◽  
Three Dimensional ◽  
Reaction Diffusion ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Black And White ◽  
Alan Turing ◽  
School Sports ◽  
The University ◽  
University Of Manchester

In his 1952 paper ‘The chemical basis of morphogenesis’ Turing postulated his now famous Morphogenesis Equation. He claimed that his theory would explain why plants and animals took the shapes they did. When I joined him, Turing suggested that I might solve his equation in three dimensions, a new problem. After many manipulations using rather sophisticated mathematics and one of the first factory-produced computers in the UK, I derived a series of solutions to Turing’s equation. I showed that these solutions explained the shapes of specimens of the marine creatures known as Radiolaria, and that they corresponded very closely to the actual spiny shapes of real radiolarians. My work provided further evidence for Turing’s theory of morphogenesis, and in particular for his belief that the external shapes exhibited by Radiolaria can be explained by his reaction–diffusion mechanism. While working in the Computing Machine Laboratory at the University of Manchester in the early 1950s, Alan Turing reignited the interests he had had in both botany and biology from his early youth. During his school-days he was more interested in the structure of the flowers on the school sports field than in the games played there (see Fig. 1.3). It is known that during the Second World War he discussed the problem of phyllotaxis (the arrangement of leaves and florets in plants), and then at Manchester he had some conversations with Claude Wardlaw, the Professor of Botany in the University. Turing was keen to take forward the work that D’Arcy Thompson had published in On Growth and Form in 1917. In his now-famous paper of 1952 Turing solved his own ‘Equation of Morphogenesis’ in two dimensions, and demonstrated a solution that could explain the ‘dappling’—the black-and-white patterns—on cows. The next step was for me to solve Turing’s equation in three dimensions. The two-dimensional case concerns only surface features of organisms, such as dappling, spots, and stripes, whereas the three-dimensional version concerns the overall shape of an organism. In 1953 I joined Turing as a research student in the University of Manchester, and he set me the task of solving his equation in three dimensions. A remarkable journey of collaboration began. Turing chatted to me in a very friendly fashion.

scholarly journals Towards a multi-physics modelling framework for thrombolysis under the influence of blood flow

2015 ◽  
Vol 12 (113) ◽  
pp. 20150949 ◽  
Author(s):  
Andris Piebalgs ◽  
X. Yun Xu
Keyword(s):  
Blood Flow ◽  
Thrombolytic Therapy ◽  
Effective Means ◽  
Reaction Diffusion ◽  
Clot Lysis ◽  
Local Flow ◽  
Pressure Drops ◽  
Modelling Framework ◽  
Internal Bleeding ◽  
Diffusion Convection

Thrombolytic therapy is an effective means of treating thromboembolic diseases but can also give rise to life-threatening side effects. The infusion of a high drug concentration can provoke internal bleeding while an insufficient dose can lead to artery reocclusion. It is hoped that mathematical modelling of the process of clot lysis can lead to a better understanding and improvement of thrombolytic therapy. To this end, a multi-physics continuum model has been developed to simulate the dissolution of clot over time upon the addition of tissue plasminogen activator (tPA). The transport of tPA and other lytic proteins is modelled by a set of reaction–diffusion–convection equations, while blood flow is described by volume-averaged continuity and momentum equations. The clot is modelled as a fibrous porous medium with its properties being determined as a function of the fibrin fibre radius and voidage of the clot. A unique feature of the model is that it is capable of simulating the entire lytic process from the initial phase of lysis of an occlusive thrombus (diffusion-limited transport), the process of recanalization, to post-canalization thrombolysis under the influence of convective blood flow. The model has been used to examine the dissolution of a fully occluding clot in a simplified artery at different pressure drops. Our predicted lytic front velocities during the initial stage of lysis agree well with experimental and computational results reported by others. Following canalization, clot lysis patterns are strongly influenced by local flow patterns, which are symmetric at low pressure drops, but asymmetric at higher pressure drops, which give rise to larger recirculation regions and extended areas of intense drug accumulation.

scholarly journals Efficient Sampling in Event-Driven Algorithms for Reaction-Diffusion Processes

2013 ◽  
Vol 13 (4) ◽  
pp. 958-984 ◽  
Author(s):  
Mohammad Hossein Bani-Hashemian ◽  
Stefan Hellander ◽  
Per Lötstedt
Keyword(s):  
Diffusion Processes ◽  
Reaction Diffusion ◽  
Three Dimensions ◽  
Cumulative Distribution ◽  
Brownian Diffusion ◽  
Time Interval ◽  
Efficient Sampling ◽  
Event Driven ◽  
Analytical Formulas ◽  
Chemically Reacting

AbstractIn event-driven algorithms for simulation of diffusing, colliding, and reacting particles, new positions and events are sampled from the cumulative distribution function (CDF) of a probability distribution. The distribution is sampled frequently and it is important for the efficiency of the algorithm that the sampling is fast. The CDF is known analytically or computed numerically. Analytical formulas are sometimes rather complicated making them difficult to evaluate. The CDF may be stored in a table for interpolation or computed directly when it is needed. Different alternatives are compared for chemically reacting molecules moving by Brownian diffusion in two and three dimensions. The best strategy depends on the dimension of the problem, the length of the time interval, the density of the particles, and the number of different reactions.

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