title: Envisioning migration: mathematics in both experimental analysis and modeling of cell behavior.
abstract: The complex nature of cell migration highlights the power and challenges of applying mathematics to biological studies. Mathematics may be used to create model equations that recapitulate migration, which can predict phenomena not easily uncovered by experiments or intuition alone. Alternatively, mathematics may be applied to interpreting complex data sets with better resolution--potentially empowering scientists to discern subtle patterns amid the noise and heterogeneity typical of migrating cells. Iteration between these two methods is necessary in order to reveal connections within the cell migration signaling network, as well as to understand the behavior that arises from those connections. Here, we review recent quantitative analysis and mathematical modeling approaches to the cell migration problem.
authors: Green Center for Systems Biology, Department of Pharmacology, Simmons Cancer Center, University of Texas Southwestern Medical Center, Dallas, TX 75390, USA. elizabeth.zhang@utsouthwestern.edu
authors: Elizabeth R
authors: ER
authors: Zhang
authors: Lani F
authors: LF
authors: Wu
authors: Steven J
authors: SJ
authors: Altschuler
mesh_terms: D000818:Animals; D002465:Cell Movement; D006801:Humans; D008433:Mathematics; D008954:Models, Biological; D015398:Signal Transduction
references: Nature. 2012 Apr 11;484(7393):233-6
references: 22498629
references: J Exp Biol. 1996 Apr;199(Pt 4):741-7
references: 8788084
references: Cell. 2007 Apr 20;129(2):411-22
references: 17448998
references: Cell. 2003 Jul 25;114(2):201-14
references: 12887922
references: J Cell Biol. 1979 Aug;82(2):517-27
references: 479314
references: PLoS Comput Biol. 2012;8(3):e1002402
references: 22396633
references: Bioinformatics. 2005 May 1;21(9):2027-35
references: 15657095
references: Nat Cell Biol. 2008 Dec;10(12):1393-400
references: 19011623
references: J Cell Sci. 1999 Sep;112 ( Pt 17):2867-74
references: 10444381
references: BMC Syst Biol. 2007 Jan 29;1:9
references: 17408516
references: PLoS Biol. 2011 May;9(5):e1000618
references: 21610858
references: Cell. 2012 May 25;149(5):1073-83
references: 22632971
references: PLoS Comput Biol. 2012;8(3):e1002392
references: 22438794
references: Cell Rep. 2013 May 30;3(5):1607-16
references: 23665220
references: Biomaterials. 2011 Oct;32(30):7524-31
references: 21782235
references: Biophys J. 2002 Jan;82(1 Pt 1):50-63
references: 11751295
references: Proc Natl Acad Sci U S A. 2013 Jan 2;110(1):129-34
references: 23251032
references: J Cell Biol. 1988 Sep;107(3):951-8
references: 2843551
references: Biophys J. 2012 Sep 19;103(6):1141-51
references: 22995486
references: Proc Natl Acad Sci U S A. 2012 Dec 26;109(52):E3668-77
references: 23185021
references: J Cell Biol. 2012 Apr 2;197(1):105-14
references: 22472441
references: Nat Cell Biol. 2011 Jun;13(6):660-7
references: 21572420
references: J Cell Sci. 2012 May 15;125(Pt 10):2381-92
references: 22344265
references: Bull Math Biol. 2006 Feb;68(2):231-53
references: 16794929
references: Wiley Interdiscip Rev Syst Biol Med. 2011 Mar-Apr;3(2):231-40
references: 21305705
references: PLoS Comput Biol. 2011 May;7(5):e1001127
references: 21573201
references: Cell. 2012 Oct 12;151(2):320-32
references: 23039994
references: Science. 2012 Apr 13;336(6078):175-9
references: 22499937
references: Proc Natl Acad Sci U S A. 2011 Dec 20;108(51):20394-9
references: 22159033
references: Annu Rev Biophys. 2010;39:265-89
references: 20192768
references: Biophys J. 2012 Sep 19;103(6):1379-89
references: 22995511
references: PLoS Biol. 2011 May;9(5):e1001059
references: 21559321
references: Bull Math Biol. 2013 Mar;75(3):393-427
references: 23358798
references: J Cell Sci. 2012 Nov 1;125(Pt 21):5138-50
references: 22899720
references: Nat Cell Biol. 2012 Aug;14(8):874-81
references: 22750946
references: Nature. 2009 Sep 3;461(7260):99-103
references: 19693013
references: Cold Spring Harb Perspect Biol. 2009 Oct;1(4):a002980
references: 20066099
references: Phys Rev E Stat Nonlin Soft Matter Phys. 2006 Dec;74(6 Pt 1):061908
references: 17280097
references: Cell. 2009 Aug 21;138(4):760-73
references: 19703401