1
|
Schindler D, Moldenhawer T, Beta C, Huisinga W, Holschneider M. Three-component contour dynamics model to simulate and analyze amoeboid cell motility in two dimensions. PLoS One 2024; 19:e0297511. [PMID: 38277351 PMCID: PMC10817190 DOI: 10.1371/journal.pone.0297511] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/27/2023] [Accepted: 01/07/2024] [Indexed: 01/28/2024] Open
Abstract
Amoeboid cell motility is relevant in a wide variety of biomedical processes such as wound healing, cancer metastasis, and embryonic morphogenesis. It is characterized by pronounced changes of the cell shape associated with expansions and retractions of the cell membrane, which result in a crawling kind of locomotion. Despite existing computational models of amoeboid motion, the inference of expansion and retraction components of individual cells, the corresponding classification of cells, and the a priori specification of the parameter regime to achieve a specific motility behavior remain challenging open problems. We propose a novel model of the spatio-temporal evolution of two-dimensional cell contours comprising three biophysiologically motivated components: a stochastic term accounting for membrane protrusions and two deterministic terms accounting for membrane retractions by regularizing the shape and area of the contour. Mathematically, these correspond to the intensity of a self-exciting Poisson point process, the area-preserving curve-shortening flow, and an area adjustment flow. The model is used to generate contour data for a variety of qualitatively different, e.g., polarized and non-polarized, cell tracks that visually resemble experimental data very closely. In application to experimental cell tracks, we inferred the protrusion component and examined its correlation to common biomarkers: the F-actin density close to the membrane and its local motion. Due to the low model complexity, parameter estimation is fast, straightforward, and offers a simple way to classify contour dynamics based on two locomotion types: the amoeboid and a so-called fan-shaped type. For both types, we use cell tracks segmented from fluorescence imaging data of the model organism Dictyostelium discoideum. An implementation of the model is provided within the open-source software package AmoePy, a Python-based toolbox for analyzing and simulating amoeboid cell motility.
Collapse
Affiliation(s)
- Daniel Schindler
- Institute of Mathematics, University of Potsdam, Potsdam, Germany
- CRC 1294 Data Assimilation, University of Potsdam, Potsdam, Germany
| | - Ted Moldenhawer
- Institute of Physics and Astronomy, University of Potsdam, Potsdam, Germany
- CRC 1294 Data Assimilation, University of Potsdam, Potsdam, Germany
| | - Carsten Beta
- Institute of Physics and Astronomy, University of Potsdam, Potsdam, Germany
- CRC 1294 Data Assimilation, University of Potsdam, Potsdam, Germany
| | - Wilhelm Huisinga
- Institute of Mathematics, University of Potsdam, Potsdam, Germany
- CRC 1294 Data Assimilation, University of Potsdam, Potsdam, Germany
| | - Matthias Holschneider
- Institute of Mathematics, University of Potsdam, Potsdam, Germany
- CRC 1294 Data Assimilation, University of Potsdam, Potsdam, Germany
| |
Collapse
|
2
|
Wu L, Feng X, He Y. Modified Characteristic Finite Element Method with Second-Order Spatial Accuracy for Solving Convection-Dominated Problem on Surfaces. ENTROPY (BASEL, SWITZERLAND) 2023; 25:1631. [PMID: 38136511 PMCID: PMC10742401 DOI: 10.3390/e25121631] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/13/2023] [Accepted: 12/05/2023] [Indexed: 12/24/2023]
Abstract
We present a modified characteristic finite element method that exhibits second-order spatial accuracy for solving convection-reaction-diffusion equations on surfaces. The temporal direction adopted the backward-Euler method, while the spatial direction employed the surface finite element method. In contrast to regular domains, it is observed that the point in the characteristic direction traverses the surface only once within a brief time. Thus, good approximation of the solution in the characteristic direction holds significant importance for the numerical scheme. In this regard, Taylor expansion is employed to reconstruct the solution beyond the surface in the characteristic direction. The stability of our scheme is then proved. A comparison is carried out with an existing characteristic finite element method based on face mesh. Numerical examples are provided to validate the effectiveness of our proposed method.
Collapse
Affiliation(s)
- Longyuan Wu
- College of Mathematics and Systems Science, Xinjiang University, Urumqi 830017, China; (L.W.); (X.F.)
| | - Xinlong Feng
- College of Mathematics and Systems Science, Xinjiang University, Urumqi 830017, China; (L.W.); (X.F.)
| | - Yinnian He
- College of Mathematics and Systems Science, Xinjiang University, Urumqi 830017, China; (L.W.); (X.F.)
- School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an 710049, China
| |
Collapse
|
3
|
Krause AL, Gaffney EA, Walker BJ. Concentration-Dependent Domain Evolution in Reaction-Diffusion Systems. Bull Math Biol 2023; 85:14. [PMID: 36637542 PMCID: PMC9839823 DOI: 10.1007/s11538-022-01115-2] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/05/2022] [Accepted: 12/24/2022] [Indexed: 01/14/2023]
Abstract
Pattern formation has been extensively studied in the context of evolving (time-dependent) domains in recent years, with domain growth implicated in ameliorating problems of pattern robustness and selection, in addition to more realistic modelling in developmental biology. Most work to date has considered prescribed domains evolving as given functions of time, but not the scenario of concentration-dependent dynamics, which is also highly relevant in a developmental setting. Here, we study such concentration-dependent domain evolution for reaction-diffusion systems to elucidate fundamental aspects of these more complex models. We pose a general form of one-dimensional domain evolution and extend this to N-dimensional manifolds under mild constitutive assumptions in lieu of developing a full tissue-mechanical model. In the 1D case, we are able to extend linear stability analysis around homogeneous equilibria, though this is of limited utility in understanding complex pattern dynamics in fast growth regimes. We numerically demonstrate a variety of dynamical behaviours in 1D and 2D planar geometries, giving rise to several new phenomena, especially near regimes of critical bifurcation boundaries such as peak-splitting instabilities. For sufficiently fast growth and contraction, concentration-dependence can have an enormous impact on the nonlinear dynamics of the system both qualitatively and quantitatively. We highlight crucial differences between 1D evolution and higher-dimensional models, explaining obstructions for linear analysis and underscoring the importance of careful constitutive choices in defining domain evolution in higher dimensions. We raise important questions in the modelling and analysis of biological systems, in addition to numerous mathematical questions that appear tractable in the one-dimensional setting, but are vastly more difficult for higher-dimensional models.
Collapse
Affiliation(s)
- Andrew L Krause
- Mathematical Sciences Department, Durham University, Upper Mountjoy Campus, Stockton Rd, Durham, DH1 3LE, UK.
| | - Eamonn A Gaffney
- Wolfson Centre for Mathematical Biology, Mathematical Institute, University of Oxford, Andrew Wiles Building, Radcliffe Observatory Quarter, Woodstock Road, Oxford, OX2 6GG, UK
| | - Benjamin J Walker
- Department of Mathematics, University College London, London, WC1H 0AY, UK
| |
Collapse
|
4
|
Chang CY, Dai ZX, Shih PJ. Modeling and simulation of cell migration on the basis of force equilibrium. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING 2022; 38:e3550. [PMID: 34719116 DOI: 10.1002/cnm.3550] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/15/2021] [Accepted: 10/26/2021] [Indexed: 06/13/2023]
Abstract
To study cell behavior, we developed a cell model to simulate cell movements and the interacting forces among cells and between cells and obstacles. The developed model simulates several cells simultaneously and examines correlations among characteristic parameters between cells and substrates during migration. We modified Odde's model to develop fundamental model, applied Gillespie's stochastic algorithm to design time during in the migration simulation, and employed Keren's membrane theory to analyze the equilibrium at the leading edges. Thus, the proposed model can analyze stresses due to substrate, the intracellular body, and the external interaction between cells and obstacles. Simulation results indicate that cell-cell interaction depends on the equilibrium between the forces at the leading edge of the membrane, namely the cell-substrate interaction force, cell-cell interaction forces, and the cell membrane force. These results also indicate that the migration direction is dependent on the resultant forces. The membrane force and substrate force directions are "low correlation," and the polymerization rate exhibits "little correlative" with the migration direction. We propose a modified cell migration model for simulating allocation and interaction among multiple cells. This model helps indicate the weightings of characteristic parameters that affect the cell migration direction and velocity.
Collapse
Affiliation(s)
- Chia-Yu Chang
- Department of Mechanical Engineering, National Taiwan University, Taipei city, Taiwan
| | - Zhi-Xuan Dai
- Department of Mechanical Engineering, National Taiwan University, Taipei city, Taiwan
| | - Po-Jen Shih
- Department of Biomedical Engineering, National Taiwan University, Taipei city, Taiwan
| |
Collapse
|
5
|
Mathematical modelling in cell migration: tackling biochemistry in changing geometries. Biochem Soc Trans 2021; 48:419-428. [PMID: 32239187 DOI: 10.1042/bst20190311] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/26/2019] [Revised: 03/05/2020] [Accepted: 03/09/2020] [Indexed: 01/18/2023]
Abstract
Directed cell migration poses a rich set of theoretical challenges. Broadly, these are concerned with (1) how cells sense external signal gradients and adapt; (2) how actin polymerisation is localised to drive the leading cell edge and Myosin-II molecular motors retract the cell rear; and (3) how the combined action of cellular forces and cell adhesion results in cell shape changes and net migration. Reaction-diffusion models for biological pattern formation going back to Turing have long been used to explain generic principles of gradient sensing and cell polarisation in simple, static geometries like a circle. In this minireview, we focus on recent research which aims at coupling the biochemistry with cellular mechanics and modelling cell shape changes. In particular, we want to contrast two principal modelling approaches: (1) interface tracking where the cell membrane, interfacing cell interior and exterior, is explicitly represented by a set of moving points in 2D or 3D space and (2) interface capturing. In interface capturing, the membrane is implicitly modelled analogously to a level line in a hilly landscape whose topology changes according to forces acting on the membrane. With the increased availability of high-quality 3D microscopy data of complex cell shapes, such methods will become increasingly important in data-driven, image-based modelling to better understand the mechanochemistry underpinning cell motion.
Collapse
|
6
|
Paquin-Lefebvre F, Xu B, DiPietro KL, Lindsay AE, Jilkine A. Pattern formation in a coupled membrane-bulk reaction-diffusion model for intracellular polarization and oscillations. J Theor Biol 2020; 497:110242. [PMID: 32179107 DOI: 10.1016/j.jtbi.2020.110242] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/26/2019] [Revised: 03/02/2020] [Accepted: 03/05/2020] [Indexed: 01/19/2023]
Abstract
Reaction-diffusion systems have been widely used to study spatio-temporal phenomena in cell biology, such as cell polarization. Coupled bulk-surface models naturally include compartmentalization of cytosolic and membrane-bound polarity molecules. Here we study the distribution of the polarity protein Cdc42 in a mass-conserved membrane-bulk model, and explore the effects of diffusion and spatial dimensionality on spatio-temporal pattern formation. We first analyze a one-dimensional (1-D) model for Cdc42 oscillations in fission yeast, consisting of two diffusion equations in the bulk domain coupled to nonlinear ODEs for binding kinetics at each end of the cell. In 1-D, our analysis reveals the existence of symmetric and asymmetric steady states, as well as anti-phase relaxation oscillations typical of slow-fast systems. We then extend our analysis to a two-dimensional (2-D) model with circular bulk geometry, for which species can either diffuse inside the cell or become bound to the membrane and undergo a nonlinear reaction-diffusion process. We also consider a nonlocal system of PDEs approximating the dynamics of the 2-D membrane-bulk model in the limit of fast bulk diffusion. In all three model variants we find that mass conservation selects perturbations of spatial modes that simply redistribute mass. In 1-D, only anti-phase oscillations between the two ends of the cell can occur, and in-phase oscillations are excluded. In higher dimensions, no radially symmetric oscillations are observed. Instead, the only instabilities are symmetry-breaking, either corresponding to stationary Turing instabilities, leading to the formation of stationary patterns, or to oscillatory Turing instabilities, leading to traveling and standing waves. Codimension-two Bogdanov-Takens bifurcations occur when the two distinct instabilities coincide, causing traveling waves to slow down and to eventually become stationary patterns. Our work clarifies the effect of geometry and dimensionality on behaviors observed in mass-conserved cell polarity models.
Collapse
Affiliation(s)
- Frédéric Paquin-Lefebvre
- Department of Mathematics and Institute of Applied Mathematics, University of British Columbia, Vancouver, Canada
| | - Bin Xu
- Department of Applied and Computational Mathematics and Statistics, University of Notre Dame, Notre Dame, IN, 46556, USA
| | - Kelsey L DiPietro
- Department of Applied and Computational Mathematics and Statistics, University of Notre Dame, Notre Dame, IN, 46556, USA; Sandia National Laboratories, NM, 46556, USA
| | - Alan E Lindsay
- Department of Applied and Computational Mathematics and Statistics, University of Notre Dame, Notre Dame, IN, 46556, USA
| | - Alexandra Jilkine
- Department of Applied and Computational Mathematics and Statistics, University of Notre Dame, Notre Dame, IN, 46556, USA.
| |
Collapse
|
7
|
Cusseddu D, Edelstein-Keshet L, Mackenzie J, Portet S, Madzvamuse A. A coupled bulk-surface model for cell polarisation. J Theor Biol 2019; 481:119-135. [DOI: 10.1016/j.jtbi.2018.09.008] [Citation(s) in RCA: 25] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/03/2018] [Revised: 09/04/2018] [Accepted: 09/07/2018] [Indexed: 10/28/2022]
|
8
|
Mackenzie JA, Nolan M, Rowlatt CF, Insall RH. An Adaptive Moving Mesh Method for Forced Curve Shortening Flow. SIAM JOURNAL ON SCIENTIFIC COMPUTING : A PUBLICATION OF THE SOCIETY FOR INDUSTRIAL AND APPLIED MATHEMATICS 2019; 41:A1170-A1200. [PMID: 31798297 PMCID: PMC6890488 DOI: 10.1137/18m1211969] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
We propose a novel adaptive moving mesh method for the numerical solution of a forced curve shortening geometric evolution equation. Control of the mesh quality is obtained using a tangential mesh velocity derived from a mesh equidistribution principle, where a positive adaptivity measure or monitor function is approximately equidistributed along the evolving curve. Central finite differences are used to discretize in space the governing evolution equation for the position vector, and a second-order implicit scheme is used for the temporal integration. Simulations are presented indicating the generation of meshes which resolve areas of high curvature and are of second-order accuracy. Furthermore, the new method delivers improved solution accuracy compared to the use of uniform arc-length meshes.
Collapse
Affiliation(s)
- J. A. Mackenzie
- Corresponding author. Department of Mathematics and Statistics, University of Strathclyde, Glasgow G1 1XH, UK ()
| | - M. Nolan
- Department of Mathematics and Statistics, University of Strathclyde, Glasgow G1 1XH, UK
| | - C. F. Rowlatt
- Department of Mathematics and Statistics, University of Strathclyde, Glasgow G1 1XH, UK
| | - R. H. Insall
- Cancer Research UK Beatson Institute, Glasgow G61 1BD, UK
| |
Collapse
|
9
|
Three-dimensional simulation of obstacle-mediated chemotaxis. Biomech Model Mechanobiol 2018; 17:1243-1268. [DOI: 10.1007/s10237-018-1023-x] [Citation(s) in RCA: 20] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/16/2017] [Accepted: 04/25/2018] [Indexed: 01/07/2023]
|
10
|
Multerer MD, Wittwer LD, Stopka A, Barac D, Lang C, Iber D. Simulation of Morphogen and Tissue Dynamics. Methods Mol Biol 2018; 1863:223-250. [PMID: 30324601 DOI: 10.1007/978-1-4939-8772-6_13] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/27/2022]
Abstract
Morphogenesis, the process by which an adult organism emerges from a single cell, has fascinated humans for a long time. Modeling this process can provide novel insights into development and the principles that orchestrate the developmental processes. This chapter focuses on the mathematical description and numerical simulation of developmental processes. In particular, we discuss the mathematical representation of morphogen and tissue dynamics on static and growing domains, as well as the corresponding tissue mechanics. In addition, we give an overview of numerical methods that are routinely used to solve the resulting systems of partial differential equations. These include the finite element method and the Lattice Boltzmann method for the discretization as well as the arbitrary Lagrangian-Eulerian method and the Diffuse-Domain method to numerically treat deforming domains.
Collapse
Affiliation(s)
- Michael D Multerer
- Department of Biosystems Science and Engineering, ETH Zurich, Basel, Switzerland
| | - Lucas D Wittwer
- Department of Biosystems Science and Engineering, ETH Zurich, Basel, Switzerland
| | - Anna Stopka
- Department of Biosystems Science and Engineering, ETH Zurich, Basel, Switzerland
| | - Diana Barac
- Department of Biosystems Science and Engineering, ETH Zurich, Basel, Switzerland
| | - Christine Lang
- Department of Biosystems Science and Engineering, ETH Zurich, Basel, Switzerland
| | - Dagmar Iber
- Department of Biosystems Science and Engineering, ETH Zurich, Basel, Switzerland.
| |
Collapse
|
11
|
Nickaeen M, Novak IL, Pulford S, Rumack A, Brandon J, Slepchenko BM, Mogilner A. A free-boundary model of a motile cell explains turning behavior. PLoS Comput Biol 2017; 13:e1005862. [PMID: 29136638 PMCID: PMC5705165 DOI: 10.1371/journal.pcbi.1005862] [Citation(s) in RCA: 24] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/07/2017] [Revised: 11/28/2017] [Accepted: 10/31/2017] [Indexed: 01/14/2023] Open
Abstract
To understand shapes and movements of cells undergoing lamellipodial motility, we systematically explore minimal free-boundary models of actin-myosin contractility consisting of the force-balance and myosin transport equations. The models account for isotropic contraction proportional to myosin density, viscous stresses in the actin network, and constant-strength viscous-like adhesion. The contraction generates a spatially graded centripetal actin flow, which in turn reinforces the contraction via myosin redistribution and causes retraction of the lamellipodial boundary. Actin protrusion at the boundary counters the retraction, and the balance of the protrusion and retraction shapes the lamellipodium. The model analysis shows that initiation of motility critically depends on three dimensionless parameter combinations, which represent myosin-dependent contractility, a characteristic viscosity-adhesion length, and a rate of actin protrusion. When the contractility is sufficiently strong, cells break symmetry and move steadily along either straight or circular trajectories, and the motile behavior is sensitive to conditions at the cell boundary. Scanning of a model parameter space shows that the contractile mechanism of motility supports robust cell turning in conditions where short viscosity-adhesion lengths and fast protrusion cause an accumulation of myosin in a small region at the cell rear, destabilizing the axial symmetry of a moving cell. To understand shapes and movements of simple motile cells, we systematically explore minimal models describing a cell as a two-dimensional actin-myosin gel with a free boundary. The models account for actin-myosin contraction balanced by viscous stresses in the actin gel and uniform adhesion. The myosin contraction causes the lamellipodial boundary to retract. Actin protrusion at the boundary counters the retraction, and the balance of protrusion and retraction shapes the cell. The models reproduce a variety of motile shapes observed experimentally. The analysis shows that the mechanical state of a cell depends on a small number of parameters. We find that when the contractility is sufficiently strong, cells break symmetry and move steadily along either straight or circular trajectory. Scanning model parameters shows that the contractile mechanism of motility supports robust cell turning behavior in conditions where deformable actin gel and fast protrusion destabilize the axial symmetry of a moving cell.
Collapse
Affiliation(s)
- Masoud Nickaeen
- Richard D. Berlin Center for Cell Analysis and Modeling, Department of Cell Biology, University of Connecticut Health Center, Farmington, CT, United States of America
| | - Igor L. Novak
- Richard D. Berlin Center for Cell Analysis and Modeling, Department of Cell Biology, University of Connecticut Health Center, Farmington, CT, United States of America
| | - Stephanie Pulford
- Center for Engineering Learning & Teaching, University of Washington, Seattle, WA, United States of America
| | - Aaron Rumack
- Department of Computer Science, Cornell University, Ithaca, NY, United States of America
| | - Jamie Brandon
- Department of Mathematics, Adrian College, Adrian, MI, United States of America
| | - Boris M. Slepchenko
- Richard D. Berlin Center for Cell Analysis and Modeling, Department of Cell Biology, University of Connecticut Health Center, Farmington, CT, United States of America
| | - Alex Mogilner
- Courant Institute and Department of Biology, New York University, New York, NY, United States of America
- * E-mail:
| |
Collapse
|
12
|
Harris PJ. A simple mathematical model of cell clustering by chemotaxis. Math Biosci 2017; 294:62-70. [PMID: 29042211 DOI: 10.1016/j.mbs.2017.10.008] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/06/2016] [Revised: 05/12/2017] [Accepted: 10/10/2017] [Indexed: 10/18/2022]
Abstract
Chemotaxis is the process by which cells and clusters of cells follow chemical signals in order to combine and form larger clusters. The spreading of the chemical signal from any given cell can be modeled using the linear diffusion equation, and the standard equations of motion can be used to determine how a cell, or cluster of cells, moves in response to the chemical signal. The resulting differential equations for the cell locations are integrated through time using the fourth-order Runge-Kutta method. The effect which changing the initial concentration magnitude, diffusion constant and velocity damping parameter has on the shape of the final clusters of cells is investigated and discussed.
Collapse
Affiliation(s)
- Paul J Harris
- School of Computing, Engineering and Mathematics, University of Brighton, UK.
| |
Collapse
|
13
|
Mackenzie JA, Nolan M, Insall RH. Local modulation of chemoattractant concentrations by single cells: dissection using a bulk-surface computational model. Interface Focus 2016; 6:20160036. [PMID: 27708760 PMCID: PMC4992739 DOI: 10.1098/rsfs.2016.0036] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/23/2022] Open
Abstract
Chemoattractant gradients are usually considered in terms of sources and sinks that are independent of the chemotactic cell. However, recent interest has focused on 'self-generated' gradients, in which cell populations create their own local gradients as they move. Here, we consider the interplay between chemoattractants and single cells. To achieve this, we extend a recently developed computational model to incorporate breakdown of extracellular attractants by membrane-bound enzymes. Model equations are parametrized, using the published estimates from Dictyostelium cells chemotaxing towards cyclic AMP. We find that individual cells can substantially modulate their local attractant field under physiologically appropriate conditions of attractant and enzymes. This means the attractant concentration perceived by receptors can be a small fraction of the ambient concentration. This allows efficient chemotaxis in chemoattractant concentrations that would be saturating without local breakdown. Similar interactions in which cells locally mould a stimulus could function in many types of directed cell motility, including haptotaxis, durotaxis and even electrotaxis.
Collapse
Affiliation(s)
- J. A. Mackenzie
- Department of Mathematics and Statistics, Universityof Strathclyde, Glasgow G1 1XH, UK
| | - M. Nolan
- Department of Mathematics and Statistics, Universityof Strathclyde, Glasgow G1 1XH, UK
| | - R. H. Insall
- Beatson Institute for Cancer Research, Switchback Road, Bearsden G61 1BD, UK
| |
Collapse
|
14
|
Tweedy L, Susanto O, Insall RH. Self-generated chemotactic gradients-cells steering themselves. Curr Opin Cell Biol 2016; 42:46-51. [PMID: 27105308 DOI: 10.1016/j.ceb.2016.04.003] [Citation(s) in RCA: 36] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/30/2016] [Accepted: 04/04/2016] [Indexed: 01/26/2023]
Abstract
Chemotaxis is a fundamentally important part of biology, but we know very little about how gradients of chemoattractant are formed. One answer is self-generated gradients, in which the moving cells break down the attractant to provide their own gradient as they migrate. Here we discuss where self-generated gradients are known, how they can be recognized, and where they are likely to be found in the future.
Collapse
Affiliation(s)
- Luke Tweedy
- Cancer Research UK Beatson Institute, Switchback Road, Bearsden G61 1BD, UK
| | - Olivia Susanto
- Cancer Research UK Beatson Institute, Switchback Road, Bearsden G61 1BD, UK
| | - Robert H Insall
- Cancer Research UK Beatson Institute, Switchback Road, Bearsden G61 1BD, UK.
| |
Collapse
|