Query: 2d simulation of chemotaxis bacteria aggregation

Candidate papers:

abstract: We start from a mathematical model which describes the collective motion of bacteria taking into account the underlying biochemistry. This model was first introduced by Keller Segel A new formulation of the system of partial differential equations is obtained by the introduction of a new variable (this new variable is similar to the quasi Fermi level in the framework of semiconductor modelling) This new system of P.D.E. is approximat ed via a mixed finite element technique. The solution algorithm is then described and finally we give some preliminary numerical results.Especially our method is well adapted to compute the concentration of bacteria.
author_names: A Marrocco
title: 2D simulation of chemotactic bacteria aggregation
year: 2002

abstract: We use the the Monte Carlo method to calculate the net displacement of an aggregation of bacteria that are under interaction and exerting each other electric forces as consequence of communications among them. Thus starting from the fact that bacterium's ions are exerting repulsion or attraction to others bacteria belonging the same population, is a cause to impulse motility or mobility of the population. It also might be a property of the whole aggregation to determine decisions that maintain their wellness and protection against antibacterial agents. We interpret the resulting solution of the diffusion's equation to model charged aggregations. From here we pass to calculate electric forces that enter inside an Monte Carlo ab initio algorithm targeting to calculate the net displacement of a population of bacteria.The resulting bacteria displacements have turned out to be dependent on the Bessel function's order.
author_names: Huber Nieto-Chaupis
title: Monte Carlo Simulation of Ab Initio NanoCommunications From Coulomb like Electric Forces in Bacteria Populations Chemotaxis
venue: 2018 IEEE XXV International Conference on Electronics, Electrical Engineering and Computing (INTERCON)
year: 2018

abstract: Cell sorting is a fundamental process that is involved in early embryo development, tumerogenesis and morphogenesis. The sorting of heterotypic cell populations is produced by a variety of inter cellular actions, e.g. differential adhesion and motility. We recently developed a software system that simulates chemotaxis based cell aggregation in 2D. The model implemented within the system includes a variety of physiological cell behaviors, such as chemical diffusion/detection, motility, proliferation, adhesion and life cycle stages. In this paper we extend the model to simulate heterotypic cell sorting. This paper provides an overview of the chemotaxis based aggregation model and describes the parameters and processes utilized to simulate the sorting of two different cell populations based on chemotactic interactions.
author_names: Manolya Eyiyurekli

Peter I Lelkes

D E Breent
title: Simulation of chemotaxis based sorting of heterotypic cell populations
venue: 2007 IEEE/NIH Life Science Systems and Applications Workshop
year: 2007

abstract: Chemotaxis is the phenomenom in which a population of cells rearranges its structure according to the behaviour of some chemical present in the environment. In this work, we consider a kinetic description of the collective motion of bacteria, incorporating the ability of cells to response to spatial and temporal variation of the gradient of the chemical. In the presence of nutriants, it has been experimentally observed the formation of concentration waves of bacteria [4] A parabolic scaling of the kinetic model allows to recover this dynamics. Then a particular attention has been given to the interactions between different species. In a hyperbolic scaling, a macroscopic model of aggregation type is derived. Blow up of regular solutions for this system is well known and a carefull analysis of measure solutions, in the sense of duality, has been obtained in one dimension [2] Numerical simulations are challenging since it implies the treatment of singular solutions including possible Dirac deltas in order to recover the dynamics of aggregates [3] This study has been recently extended in dimension greater than one [1] thanks to the notion of the Filippov flow for transport equations with singular velocity field.
author_names: Nicolas Vauchelet
title: MATHEMATICAL DESCRIPTION OF BACTERIAL MOTION BY CHEMOTAXIS AGGREGATION AND WAVES OF CONCENTRATION
year: 2015

abstract: The ability to navigate in chemical gradients, called chemotaxis, is crucial for the survival of microorganisms. It allows them to find food and to escape from toxins. Many microorganisms can produce the chemicals to which they respond themselves and use chemotaxis for signaling, which can be seen as a basic form of communication, allowing ensembles of microorganisms to coordinate their behavior, for example, during embryogenesis, biofilm formation, or cellular aggregation. For example, Dictyostelium cells use signaling as a survival strategy: when starving, they produce certain chemicals toward which other cells show taxis. This leads to aggregation of the cells resulting in a multicellular aggregate that can sustain long starvation periods. Remarkably, the past decade has led to the development of synthetic microswimmers, which can self propel through a solvent, analogously to bacteria and other microorganisms. The mechanism underlying the self propulsion of synthetic microswimmers like camphor boats, droplet swimmers, and in particular autophoretic Janus colloids involves the production of certain chemicals. As we will discuss in this Account, the same chemicals (phoretic fields) involved in the self propulsion of a (Janus) microswimmer also act on other ones and bias their swimming direction toward (or away from) the producing microswimmer. Synthetic microswimmers therefore provide a synthetic analogue to motile microorganisms interacting by taxis toward (or away from) self produced chemical fields. In this Account, we review recent progress in the theoretical description of synthetic chemotaxis mainly based on simulations and field theoretical descriptions. We will begin with single motile particles leaving chemical trails behind with which they interact themselves, leading to effects like self trapping or self avoidance. Besides these self interactions, in ensembles of synthetic motile particles each particle also responds to the chemicals produced by other particles, inducing chemical (or phoretic) cross interactions. When these interactions are attractive, they commonly lead to clusters, even at low particle density. These clusters may either proceed toward macrophase separation, resembling Dictyostelium aggregation, or, as shown very recently, lead to dynamic clusters of self limited size (dynamic clustering) as seen in experiments in autophoretic Janus colloids. Besides the classical case where chemical interactions are attractive, this Account discusses, as its main focus, repulsive chemical interactions, which can create a new and less known avenue to pattern formation in active systems leading to a variety of pattern, including clusters which are surrounded by shells of chemicals, traveling waves and more complex continuously reshaping patterns. In all these cases "synthetic signalling" can crucially determine the collective behavior of synthetic microswimmer ensembles and can be used as a design principle to create patterns in motile active particles.
author_names: Benno Liebchen

Hartmut Lowen
title: Synthetic Chemotaxis and Collective Behavior in Active Matter.
venue: Accounts of chemical research
year: 2018

abstract: Complex bioconvection patterns have been studied analytically, experimentally, and numerically previously only for a flat free surface of a suspension of chemotaxis bacteria in a shallow/deep chamber. In this paper, we have considered a two dimensional chemotaxis diffusion convection system with a deformed free surface. The influence of aggregation of chemotactic cells on the deformed free surface of a shallow chamber is studied analytically. The aim of this paper is to investigate the nature of the instability in the chemotaxis diffusion convection system. We performed a detailed linear stability analysis of a steady state cell and oxygen concentration distribution. The system becomes dominated by nonlinear convection terms beyond a critical Rayleigh number Rat, which also depends on the critical wavenumber k as well as the other parameters. We have investigated that how the critical Rayleigh number in this system varies with three different sets of parameters. A weakly nonlinear analysis is carried out as well to determine the relative stability of the pattern formation at the onset of instability. A reactance between rolls, squares, hexagons, and mixed mode pattern is investigated in detail. Further research should link the weakly nonlinear analysis with the bifurcation analysis. Some important direct numerical simulation results have been presented in the support of linear stability analysis. Comparison of the analytical steady state solution shows good agreement with the numerical result.
author_names: Symphony Chakraborty

Filip Ivancic

Maxim A Solovchuk

Tony W H Sheu
title: Stability and dynamics of a chemotaxis system with deformed free surface in a shallow chamber
year: 2018

abstract: Abstract In this paper, the chemotaxis partial differential equations models which describe the movement by one community in reaction to one chemical or biological signal are given and solved numerically on surfaces. The models and the numerical method concerned are in terms of a generic form of chemotaxis models. We develop a new semi implicit finite element scheme based on the gradient and Laplacian recoveries to linearize the equations. Meanwhile, we modify the proposed semi implicit scheme as a characteristic form and present a novel strategy for the discretization of characteristic derivative on surface. The lumped mass modification is employed for positivity preservation. And the related analysis results are provided. We investigate the accuracy and convergence of the proposed method by numerical tests. And the simulations of blowing up solution, pattern formulations and aggregations of bacteria demonstrate the applicability of the proposed methods.
author_names: Xufeng Xiao

Xinlong Feng

Yinnian He
title: Numerical simulations for the chemotaxis models on surfaces via a novel characteristic finite element method
venue: Comput. Math. Appl.
year: 2019

abstract: We have developed a software system that simulates chemotaxis based cell aggregation in 2D. The model implemented within the system consists of such cell behaviors as chemical diffusion/detection, motility, proliferation, adhesion and life cycle stages. Each virtual cell detects the state of the environment, and responds to the environment based on a pre defined "program" and its own internal state. Cells are discrete units that are located on a grid, exist in discrete states (e.g. active or dying) and perform discrete tasks (e.g. divide and attach) but they also contain and are affected by continuous quantities (e.g. chemoattractant concentrations, gradients, age and velocities) This paper provides an overview of our chemotaxis based aggregation model and details the algorithms required to perform chemotaxis based cell aggregation simulation. A number of biological studies are being conducted with the system. They include fine tuning the model parameters to reproduce in vitro PC12 cell aggregation experiments and parametric studies that demonstrate the effect that the model's components have on cell aggregation dynamics.
author_names: Manolya Eyiyurekli

Peter I Lelkes

David E Breen
title: A Computational System for Investigating Chemotaxis Based Cell Aggregation
venue: ECAL
year: 2007

abstract: We present a new algorithm based on a Cartesian mesh for the numerical approximation of kinetic models for chemosensitive movements set in an arbitrary geometry. We investigate the influence of the geometry on the collective behavior of bacteria described by a kinetic equation interacting with nutrients and chemoattractants. Numerical simulations are performed to verify accuracy and stability of the scheme and its ability to exhibit aggregation of cells and wave propagations. Finally, some comparisons with experiments show the robustness and accuracy of such kinetic models.
author_names: Francis Filbet

Chang Yang
title: Numerical Simulations of Kinetic Models for Chemotaxis
venue: SIAM J. Sci. Comput.
year: 2014

abstract: Understanding the collective motion of self propelling organisms in confined geometries, such as that of narrow channels, is of great theoretical and practical importance. By means of numerical simulations we study the motion of model bacteria in 2D channels under different flow conditions: fluid at rest, steady and unsteady flow. We find aggregation of bacteria near channel walls and, in the presence of external flow, also upstream swimming, which turns out to be a very robust result. Detailed analysis of bacterial velocity and orientation fields allows us to quantify the phenomenon by varying cell density, channel width and fluid velocity. The tumbling mechanism turns out to have strong influence on velocity profiles and particle flow, resulting in a net upstream flow in the case of non tumbling organisms. Finally we demonstrate that upstream flow can be enhanced by a suitable choice of an unsteady flow pattern.
author_names: Andrea Costanzo

Roberto Di Leonardo

Giancarlo Ruocco

Luca Angelani
title: Transport of self propelling bacteria in micro channel flow.
venue: Journal of physics. Condensed matter an Institute of Physics journal
year: 2012