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Cited by 23Cellular Mechanics and InteractionsMathematical Biology Tumor GrowthElectromagnetic Fields and Biological Effects

Quantifying the roles of random motility and directed motility using advection-diffusion theory for a 3T3 fibroblast cell migration assay stimulated with an electric field

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Simpson, Matthew J., Lo, Kai-Yin, Sun, Yung-Shin·2017·BMC Systems Biology
DOI 10.1186/s12918-017-0413-5PMC PMC5356249
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Abstract

BACKGROUND: Directed cell migration can be driven by a range of external stimuli, such as spatial gradients of: chemical signals (chemotaxis); adhesion sites (haptotaxis); or temperature (thermotaxis). Continuum models of cell migration typically include a diffusion term to capture the undirected component of cell motility and an advection term to capture the directed component of cell motility. However, there is no consensus in the literature about the form that the advection term takes. Some theoretical studies suggest that the advection term ought to include receptor saturation effects. However, others adopt a much simpler constant coefficient. One of the limitations of including receptor saturation effects is that it introduces several additional unknown parameters into the model. Therefore, a relevant research question is to investigate whether directed cell migration is best described by a simple constant tactic coefficient or a more complicated model incorporating saturation effects. RESULTS: We study directed cell migration using an experimental device in which the directed component of the cell motility is driven by a spatial gradient of electric potential, which is known as electrotaxis. The electric field (EF) is proportional to the spatial gradient of the electric potential. The spatial variation of electric potential across the experimental device varies in such a way that there are several subregions on the device in which the EF takes on different values that are approximately constant within those subregions. We use cell trajectory data to quantify the motion of 3T3 fibroblast cells at different locations on the device to examine how different values of the EF influences cell motility. The undirected (random) motility of the cells is quantified in terms of the cell diffusivity, D, and the directed motility is quantified in terms of a cell drift velocity, v. Estimates D and v are obtained under a range of four different EF conditions, which correspond to normal physiological conditions. Our results suggest that there is no anisotropy in D, and that D appears to be approximately independent of the EF and the electric potential. The drift velocity increases approximately linearly with the EF, suggesting that the simplest linear advection term, with no additional saturation parameters, provides a good explanation of these physiologically relevant data. CONCLUSIONS: We find that the simplest linear advection term in a continuum model of directed cell motility is sufficient to describe a range of different electrotaxis experiments for 3T3 fibroblast cells subject to normal physiological values of the electric field. This is useful information because alternative models that include saturation effects involve additional parameters that need to be estimated before a partial differential equation model can be applied to interpret or predict a cell migration experiment.

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  • Variational System Identification has been applied to identify governing equations for the evolution of materials, the spatiotemporal spread of COVID-19, and constitutive models of soft materials.

    “Variational System Identification has been applied to identify governing equations for the evolution of materials17,20,19, the spatiotemporal spread of COVID-1921,18, as well as constitutive models of soft materials22,23.”

    From Inference of weak-form partial differential equations describing migration and proliferation mechanisms in wound healing experiments on cancer cells (2025) · cites this paper as [17]

    The Background and Methods > Modelling methods sections describe a 3T3 fibroblast migration assay using an advection–diffusion model. Our copy does not address Variational System Identification or its applications to material evolution, COVID-19 spread, or soft-material constitutive models (searched those terms); page numbers were not available. (LLM, conf=0.77)

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  • Variational System Identification extends SINDy to inferring PDEs in weak form, thereby offering advantages in the presence of noise and high derivatives.

    “It extends the popular SINDy approach12,13,14,15,16 to inferring PDEs in weak form, thereby offering advantages in the presence of noise and high derivatives17,18,19.”

    From Inference of weak-form partial differential equations describing migration and proliferation mechanisms in wound healing experiments on cancer cells (2025) · cites this paper as [17]

    The Background and Modelling methods passages describe an advection-diffusion model for cell migration, not Variational System Identification. Searches for SINDy, weak-form PDE inference, noise, and high derivatives found no passage addressing the attributed claim. (LLM, conf=0.78)

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Cited by

Sorted by citations

Authors
Simpson, M. J., Lo, K.-Y., & Sun, Y.-S.
Affiliations
  • Queensland University of Technology (AU)
  • National Taiwan University (TW)
  • Fu Jen Catholic University (TW)
Corresponding author
Simpson, Matthew J.
ORCID
Venue
BMC Systems Biology
Publisher
Springer Science and Business Media LLC
Published
2017-03-17
Volume
11
Issue
1
Pages
39-39
ISSN
1752-0509 (ISSN-L)
DOI
10.1186/s12918-017-0413-5
PMC
PMC5356249
OpenAlex
W2596480873
Cited by
23
References
1
Citations by year
2026: 3 · 2024: 1 · 2023: 3 · 2022: 3 · 2021: 5 · 2020: 3 · 2019: 2 · 2018: 2 · 2017: 1
FWCI
1.17
Type
journal article
Language
en
Open access
Licence
Locations
  • BMC Systems Biology (publishedVersion, cc-by)
  • PubMed Central (publishedVersion, cc-by)
  • PubMed (publishedVersion)
Funders
  • Australian Research Countil (DP170100474)
  • Australian Research Council (DP140100249)
Topics
  • Life Sciences › Biochemistry, Genetics and Molecular Biology › Cell Biology › Cellular Mechanics and Interactions
  • Physical Sciences › Mathematics › Modeling and Simulation › Mathematical Biology Tumor Growth
  • Life Sciences › Biochemistry, Genetics and Molecular Biology › Biophysics › Electromagnetic Fields and Biological Effects
Keywords
electrotaxis, directed cell migration, random motility, advection-diffusion model, 3T3 fibroblasts, electric field, drift velocity, receptor saturation, cell migration assay, parameter estimation
MeSH terms
Animals, Cell Movement, Diffusion, Electricity, Models, Biological, 3T3 Cells, Mice, Cell Migration Assays

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