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
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 com...
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| Published in | BMC systems biology Vol. 11; no. 1; p. 39 |
|---|---|
| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
London
BioMed Central
17.03.2017
|
| Subjects | |
| Online Access | Get full text |
| ISSN | 1752-0509 1752-0509 |
| DOI | 10.1186/s12918-017-0413-5 |
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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. |
|---|---|
| AbstractList | 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.
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.
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. 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.BACKGROUNDDirected 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.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.RESULTSWe 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.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.CONCLUSIONSWe 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. 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. 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. |
| ArticleNumber | 39 |
| Author | Sun, Yung-Shin Lo, Kai-Yin Simpson, Matthew J. |
| Author_xml | – sequence: 1 givenname: Matthew J. orcidid: 0000-0001-6254-313X surname: Simpson fullname: Simpson, Matthew J. email: matthew.simpson@qut.edu.au organization: School of Mathematical Sciences, Queensland University of Technology (QUT) – sequence: 2 givenname: Kai-Yin surname: Lo fullname: Lo, Kai-Yin organization: Department of Agricultural Chemistry, National Taiwan University – sequence: 3 givenname: Yung-Shin surname: Sun fullname: Sun, Yung-Shin organization: Department of Physics, Fu-Jen Catholic University |
| BackLink | https://www.ncbi.nlm.nih.gov/pubmed/28302111$$D View this record in MEDLINE/PubMed |
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| Cites_doi | 10.1016/j.bbrc.2011.07.004 10.1016/j.jtbi.2015.10.040 10.1016/j.jtbi.2006.06.021 10.1063/1.2952290 10.1093/imammb/dql007 10.1098/rsif.2008.0014 10.1016/j.physa.2008.10.038 10.1063/1.4932662 10.1089/107632704323061834 10.1083/jcb.17.2.299 10.1083/jcb.106.2.303 10.1002/bit.260370707 10.1098/rsif.2013.0007 10.1016/j.bioelechem.2012.08.002 10.1186/s12918-015-0182-y 10.1016/0022-5193(71)90050-6 10.1016/S0167-2789(98)00272-3 10.1016/j.physa.2015.08.049 10.1063/1.4896296 10.1088/0951-7715/23/8/008 10.1006/exer.2000.0830 10.1137/130923129 10.1016/S0022-5193(03)00258-3 10.1002/bit.260370708 10.1016/j.jtbi.2006.10.024 10.1083/jcb.101.6.2023 10.1088/0960-1317/15/6/005 10.1016/j.physd.2007.10.003 10.1016/j.semcdb.2008.12.009 10.1002/cm.970110102 10.1016/S0070-2153(03)58001-2 10.1098/rspb.1990.0061 10.1016/j.ceb.2012.01.001 10.1088/1367-2630/16/2/025002 10.1016/j.jtbi.2014.04.026 10.1007/s11538-005-9028-x 10.1093/imammb/17.4.395 10.1007/b98868 10.1242/jcs.99.2.419 10.1016/S0022-5193(05)80201-2 10.1242/jcs.01125 10.1016/j.snb.2003.10.022 |
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| Keywords | Random motility Keller-Segal model Directed motility Cell migration Partial differential equation Electrotaxis |
| Language | English |
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| References | MJ Simpson (413_CR37) 2013; 75 GJ Pettet (413_CR29) 2000; 17 KR Robinson (413_CR11) 1985; 101 CL Stokes (413_CR27) 1991; 99 JA Sherratt (413_CR1) 1990; 241 M Zhao (413_CR16) 2009; 20 RM Ford (413_CR25) 1991; 37 BP Marchant (413_CR21) 2006; 23 JY Cheng (413_CR39) 2004; 99 JC Vanegas-Acosta (413_CR13) 2012; 88 M Wechselberger (413_CR30) 2010; 23 SK Hughes-Alford (413_CR18) 2012; 24 RT Tranquillo (413_CR20) 1988; 11 MJ Simpson (413_CR45) 2013; 10 ME Mycielska (413_CR12) 2004; 117 SY Wu (413_CR35) 2015; 9 AQ Cai (413_CR36) 2007; 245 RA Gatenby (413_CR4) 1996; 56 N Charteris (413_CR32) 2014; 16 EF Keller (413_CR6) 1971; 30 R Nuccitelli (413_CR14) 2003; 58 K Harley (413_CR31) 2014; 13 HS Hou (413_CR42) 2014; 8 MJ Simpson (413_CR10) 2007; 243 CL Stokes (413_CR28) 1991; 152 JY Cheng (413_CR40) 2005; 15 KA Landman (413_CR22) 2008; 237 MJ Simpson (413_CR44) 2009; 388 JD Murray (413_CR7) 2002 D Wu (413_CR23) 2011; 411 B Farboud (413_CR15) 2000; 70 AQ Cai (413_CR9) 2006; 68 RT Tranquillo (413_CR19) 1988; 106 GJ Todaro (413_CR34) 1963; 17 RM Ford (413_CR26) 1991; 37 JY Cheng (413_CR41) 2008; 2 C Irons (413_CR33) 2016; 442 W Jin (413_CR17) 2016; 390 AJ Perumpanani (413_CR24) 1999; 126 RB Bird (413_CR38) 2005 KJ Painter (413_CR8) 2003; 225 EA Codling (413_CR43) 2008; 5 PK Maini (413_CR2) 2004; 10 ST Johnston (413_CR5) 2015; 9 KK Treloar (413_CR3) 2014; 356 26188761 - BMC Syst Biol. 2015 Jul 19;9:38 16904698 - J Theor Biol. 2006 Dec 7;243(3):343-60 19693408 - Biomicrofluidics. 2008 Jun 17;2(2):24105 18600657 - Biotechnol Bioeng. 1991 Mar 25;37(7):661-72 14604585 - J Theor Biol. 2003 Dec 7;225(3):327-39 13985244 - J Cell Biol. 1963 May;17:299-313 3208295 - Cell Motil Cytoskeleton. 1988;11(1):1-15 14711011 - Curr Top Dev Biol. 2003;58:1-26 22284347 - Curr Opin Cell Biol. 2012 Apr;24(2):284-91 11270751 - IMA J Math Appl Med Biol. 2000 Dec;17(4):395-413 23584951 - Bull Math Biol. 2013 May;75(5):871-89 10870525 - Exp Eye Res. 2000 May;70(5):667-73 4926701 - J Theor Biol. 1971 Feb;30(2):225-34 26487906 - Biomicrofluidics. 2015 Oct 06;9(5):054120 3339093 - J Cell Biol. 1988 Feb;106(2):303-9 15075225 - J Cell Sci. 2004 Apr 1;117(Pt 9):1631-9 23427098 - J R Soc Interface. 2013 Feb 20;10(82):20130007 8971186 - Cancer Res. 1996 Dec 15;56(24):5745-53 3905820 - J Cell Biol. 1985 Dec;101(6):2023-7 1885678 - J Cell Sci. 1991 Jun;99 ( Pt 2):419-30 19146969 - Semin Cell Dev Biol. 2009 Aug;20(6):674-82 18426776 - J R Soc Interface. 2008 Aug 6;5(25):813-34 18600656 - Biotechnol Bioeng. 1991 Mar 25;37(7):647-60 16627537 - Math Med Biol. 2006 Sep;23(3):173-96 1721100 - J Theor Biol. 1991 Oct 7;152(3):377-403 24787651 - J Theor Biol. 2014 Sep 7;356:71-84 22944767 - Bioelectrochemistry. 2012 Dec;88:134-43 26646767 - J Theor Biol. 2016 Feb 7;390:136-45 16794920 - Bull Math Biol. 2006 Jan;68(1):25-52 15165464 - Tissue Eng. 2004 Mar-Apr;10(3-4):475-82 17188306 - J Theor Biol. 2007 Apr 7;245(3):576-94 1978332 - Proc Biol Sci. 1990 Jul 23;241(1300):29-36 21782800 - Biochem Biophys Res Commun. 2011 Aug 12;411(4):695-701 |
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Biomicrofluidics doi: 10.1063/1.4932662 – volume: 10 start-page: 475 year: 2004 ident: 413_CR2 publication-title: Tissue Eng doi: 10.1089/107632704323061834 – volume: 17 start-page: 299 year: 1963 ident: 413_CR34 publication-title: J Cell Biol doi: 10.1083/jcb.17.2.299 – volume: 106 start-page: 303 year: 1988 ident: 413_CR19 publication-title: J Cell Biol doi: 10.1083/jcb.106.2.303 – volume: 37 start-page: 647 year: 1991 ident: 413_CR25 publication-title: Biotechnol Bioeng doi: 10.1002/bit.260370707 – volume: 10 start-page: 130007 year: 2013 ident: 413_CR45 publication-title: J R Soc Interface doi: 10.1098/rsif.2013.0007 – volume: 56 start-page: 5745 year: 1996 ident: 413_CR4 publication-title: Cancer Res – volume: 88 start-page: 134 year: 2012 ident: 413_CR13 publication-title: Bioelectrochemistry doi: 10.1016/j.bioelechem.2012.08.002 – volume: 9 start-page: 38 year: 2015 ident: 413_CR5 publication-title: BMC Syst Biol doi: 10.1186/s12918-015-0182-y – volume: 30 start-page: 225 year: 1971 ident: 413_CR6 publication-title: J Theor Biol doi: 10.1016/0022-5193(71)90050-6 – volume: 126 start-page: 145 year: 1999 ident: 413_CR24 publication-title: Physica D doi: 10.1016/S0167-2789(98)00272-3 – volume: 442 start-page: 110 year: 2016 ident: 413_CR33 publication-title: Physica A doi: 10.1016/j.physa.2015.08.049 – volume: 8 start-page: 052007 year: 2014 ident: 413_CR42 publication-title: Biomicrofluidics doi: 10.1063/1.4896296 – volume: 23 start-page: 1949 year: 2010 ident: 413_CR30 publication-title: Nonlinearity doi: 10.1088/0951-7715/23/8/008 – volume: 70 start-page: 667 year: 2000 ident: 413_CR15 publication-title: Exp Eye Res doi: 10.1006/exer.2000.0830 – volume: 13 start-page: 366 year: 2014 ident: 413_CR31 publication-title: SIAM J Appl Dyn Syst doi: 10.1137/130923129 – volume: 225 start-page: 327 year: 2003 ident: 413_CR8 publication-title: J Theor Biol doi: 10.1016/S0022-5193(03)00258-3 – volume: 37 start-page: 661 year: 1991 ident: 413_CR26 publication-title: Biotechnol Bioeng doi: 10.1002/bit.260370708 – volume: 245 start-page: 576 year: 2007 ident: 413_CR36 publication-title: J Theor Biol doi: 10.1016/j.jtbi.2006.10.024 – volume: 75 start-page: 871 year: 2013 ident: 413_CR37 publication-title: Bull Math Model – volume: 101 start-page: 2023 year: 1985 ident: 413_CR11 publication-title: J Cell Biol doi: 10.1083/jcb.101.6.2023 – volume: 15 start-page: 1147 year: 2005 ident: 413_CR40 publication-title: J Micromech Microeng doi: 10.1088/0960-1317/15/6/005 – volume: 237 start-page: 678 year: 2008 ident: 413_CR22 publication-title: Physica D doi: 10.1016/j.physd.2007.10.003 – volume: 20 start-page: 674 year: 2009 ident: 413_CR16 publication-title: Semin Cell Dev Biol doi: 10.1016/j.semcdb.2008.12.009 – volume: 11 start-page: 1 year: 1988 ident: 413_CR20 publication-title: Cell Motil Cytoskel doi: 10.1002/cm.970110102 – volume: 58 start-page: 1 year: 2003 ident: 413_CR14 publication-title: Curr Top Dev Biol doi: 10.1016/S0070-2153(03)58001-2 – volume: 241 start-page: 29 year: 1990 ident: 413_CR1 publication-title: Proc R Soc Lond B doi: 10.1098/rspb.1990.0061 – volume: 24 start-page: 284 year: 2012 ident: 413_CR18 publication-title: Curr Opin Cell Biol doi: 10.1016/j.ceb.2012.01.001 – volume: 16 start-page: 025002 year: 2014 ident: 413_CR32 publication-title: New J Phys doi: 10.1088/1367-2630/16/2/025002 – volume: 356 start-page: 71 year: 2014 ident: 413_CR3 publication-title: J Theor Biol doi: 10.1016/j.jtbi.2014.04.026 – volume: 68 start-page: 25 year: 2006 ident: 413_CR9 publication-title: Bull Math Biol doi: 10.1007/s11538-005-9028-x – volume: 17 start-page: 395 year: 2000 ident: 413_CR29 publication-title: Math Med Biol doi: 10.1093/imammb/17.4.395 – volume-title: Mathematical biology: i an introduction year: 2002 ident: 413_CR7 doi: 10.1007/b98868 – volume: 99 start-page: 419 year: 1991 ident: 413_CR27 publication-title: J Cell Sci doi: 10.1242/jcs.99.2.419 – volume: 152 start-page: 377 year: 1991 ident: 413_CR28 publication-title: J Theor Biol doi: 10.1016/S0022-5193(05)80201-2 – volume: 117 start-page: 1631 year: 2004 ident: 413_CR12 publication-title: J Cell Sci doi: 10.1242/jcs.01125 – volume: 99 start-page: 186 year: 2004 ident: 413_CR39 publication-title: Sensor Actuat B-Chem doi: 10.1016/j.snb.2003.10.022 – reference: 16627537 - Math Med Biol. 2006 Sep;23(3):173-96 – reference: 16904698 - J Theor Biol. 2006 Dec 7;243(3):343-60 – reference: 4926701 - J Theor Biol. 1971 Feb;30(2):225-34 – reference: 18600657 - Biotechnol Bioeng. 1991 Mar 25;37(7):661-72 – reference: 14604585 - J Theor Biol. 2003 Dec 7;225(3):327-39 – reference: 19693408 - Biomicrofluidics. 2008 Jun 17;2(2):24105 – reference: 17188306 - J Theor Biol. 2007 Apr 7;245(3):576-94 – reference: 3208295 - Cell Motil Cytoskeleton. 1988;11(1):1-15 – reference: 8971186 - Cancer Res. 1996 Dec 15;56(24):5745-53 – reference: 14711011 - Curr Top Dev Biol. 2003;58:1-26 – reference: 15075225 - J Cell Sci. 2004 Apr 1;117(Pt 9):1631-9 – reference: 3339093 - J Cell Biol. 1988 Feb;106(2):303-9 – reference: 23584951 - Bull Math Biol. 2013 May;75(5):871-89 – reference: 21782800 - Biochem Biophys Res Commun. 2011 Aug 12;411(4):695-701 – reference: 16794920 - Bull Math Biol. 2006 Jan;68(1):25-52 – reference: 18426776 - J R Soc Interface. 2008 Aug 6;5(25):813-34 – reference: 3905820 - J Cell Biol. 1985 Dec;101(6):2023-7 – reference: 15165464 - Tissue Eng. 2004 Mar-Apr;10(3-4):475-82 – reference: 1721100 - J Theor Biol. 1991 Oct 7;152(3):377-403 – reference: 1978332 - Proc Biol Sci. 1990 Jul 23;241(1300):29-36 – reference: 24787651 - J Theor Biol. 2014 Sep 7;356:71-84 – reference: 13985244 - J Cell Biol. 1963 May;17:299-313 – reference: 23427098 - J R Soc Interface. 2013 Feb 20;10(82):20130007 – reference: 11270751 - IMA J Math Appl Med Biol. 2000 Dec;17(4):395-413 – reference: 26646767 - J Theor Biol. 2016 Feb 7;390:136-45 – reference: 19146969 - Semin Cell Dev Biol. 2009 Aug;20(6):674-82 – reference: 1885678 - J Cell Sci. 1991 Jun;99 ( Pt 2):419-30 – reference: 18600656 - Biotechnol Bioeng. 1991 Mar 25;37(7):647-60 – reference: 26487906 - Biomicrofluidics. 2015 Oct 06;9(5):054120 – reference: 26188761 - BMC Syst Biol. 2015 Jul 19;9:38 – reference: 22284347 - Curr Opin Cell Biol. 2012 Apr;24(2):284-91 – reference: 10870525 - Exp Eye Res. 2000 May;70(5):667-73 – reference: 22944767 - Bioelectrochemistry. 2012 Dec;88:134-43 |
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| Snippet | Background
Directed cell migration can be driven by a range of external stimuli, such as spatial gradients of: chemical signals (chemotaxis); adhesion sites... Directed cell migration can be driven by a range of external stimuli, such as spatial gradients of: chemical signals (chemotaxis); adhesion sites (haptotaxis);... Background Directed cell migration can be driven by a range of external stimuli, such as spatial gradients of: chemical signals (chemotaxis); adhesion sites... |
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| SubjectTerms | 3T3 Cells Advection Algorithms Animals Anisotropy Bioinformatics Biomedical and Life Sciences Cell adhesion & migration Cell culture Cell growth Cell migration Cell Migration Assays Cell Movement Cellular and Medical Topics Chemotaxis Computational Biology/Bioinformatics Continuum modeling Diffusion Diffusion theory Drift Drift estimation Electric fields Electric potential Electricity External stimuli Fibroblasts Life Sciences Mathematical models Methods Mice Models, Biological Motility Parameter estimation Partial differential equations Physiological Physiological effects Physiology Receptors Research Article Saturation Simulation and Modeling software and technology Spatial data Systems Biology Temperature effects Thermotaxis Velocity |
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| Title | 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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