title: Mathematics and biology: a Kantian view on the history of pattern formation theory.
abstract: Driesch's statement, made around 1900, that the physics and chemistry of his day were unable to explain self-regulation during embryogenesis was correct and could be extended until the year 1972. The emergence of theories of self-organisation required progress in several areas including chemistry, physics, computing and cybernetics. Two parallel lines of development can be distinguished which both culminated in the early 1970s. Firstly, physicochemical theories of self-organisation arose from theoretical (Lotka 1910-1920) and experimental work (Bray 1920; Belousov 1951) on chemical oscillations. However, this research area gained broader acceptance only after thermodynamics was extended to systems far from equilibrium (1922-1967) and the mechanism of the prime example for a chemical oscillator, the Belousov-Zhabotinski reaction, was deciphered in the early 1970s. Secondly, biological theories of self-organisation were rooted in the intellectual environment of artificial intelligence and cybernetics. Turing wrote his The chemical basis of morphogenesis (1952) after working on the construction of one of the first electronic computers. Likewise, Gierer and Meinhardt's theory of local activation and lateral inhibition (1972) was influenced by ideas from cybernetics. The Gierer-Meinhardt theory provided an explanation for the first time of both spontaneous formation of spatial order and of self-regulation that proved to be extremely successful in elucidating a wide range of patterning processes. With the advent of developmental genetics in the 1980s, detailed molecular and functional data became available for complex developmental processes, allowing a new generation of data-driven theoretical approaches. Three examples of such approaches will be discussed. The successes and limitations of mathematical pattern formation theory throughout its history suggest a picture of the organism, which has structural similarity to views of the organic world held by the philosopher Immanuel Kant at the end of the eighteenth century.
authors.affiliation: Institute of Developmental Biology, University of Cologne, Biowissenschaftliches Zentrum, Zülpicher Strasse 47b, 50674 Cologne, Germany. Siegfried.Roth@uni-koeln.de
authors.forename: Siegfried
authors.initials: S
authors.lastname: Roth
mesh_terms: D000818:Animals; D019521:Body Patterning; D055598:Chemical Phenomena; D015509:Developmental Biology / Q000266:history; D004330:Drosophila / Q000235:genetics / Q000254:growth & development; D049672:History, 19th Century; D049673:History, 20th Century; D008432:Mathematical Computing; D008954:Models, Biological; D009024:Morphogenesis; D013816:Thermodynamics
references.citation: Nature. 1959 Jun 13;183(4676):1654-5
references.pmid: 13666847
references.citation: Mech Dev. 1993 Sep;43(1):3-19
references.pmid: 8240970
references.citation: Kybernetik. 1972 Dec;12(1):30-9
references.pmid: 4663624
references.citation: Proc R Soc Lond B Biol Sci. 1960 Jun 14;152:397-409
references.pmid: 13854863
references.citation: J Cell Sci. 1999 Sep;112 ( Pt 17):2867-74
references.pmid: 10444381
references.citation: Genetics. 2004 Aug;167(4):1721-37
references.pmid: 15342511
references.citation: J Theor Biol. 1991 Oct 21;152(4):429-53
references.pmid: 1758194
references.citation: Development. 1990 Nov;110(3):759-67
references.pmid: 2088718
references.citation: Dev Biol. 2010 Sep 1;345(1):12-7
references.pmid: 20580703
references.citation: Cell. 1988 Jul 1;54(1):95-104
references.pmid: 3383245
references.citation: Prog Biophys Mol Biol. 1981;37(1):1-47
references.pmid: 7244249
references.citation: Nature. 1999 Apr 1;398(6726):427-31
references.pmid: 10201373
references.citation: Nature. 1992 Apr 16;356(6370):610-2
references.pmid: 1348571
references.citation: PLoS Comput Biol. 2009 Mar;5(3):e1000303
references.pmid: 19282965
references.citation: Development. 1987 Sep;101(1):1-22
references.pmid: 2896587
references.citation: Genetics. 1989 Jan;121(1):101-17
references.pmid: 2492966
references.citation: Cell. 1992 Oct 30;71(3):451-61
references.pmid: 1423606
references.citation: Development. 2010 Sep 1;137(17):2857-62
references.pmid: 20699297
references.citation: Nature. 2002 Sep 19;419(6904):304-8
references.pmid: 12239569
references.citation: Bioessays. 2000 Aug;22(8):753-60
references.pmid: 10918306
references.citation: Dev Biol. 2007 Dec 15;312(2):623-30
references.pmid: 18001703
references.citation: Dev Cell. 2010 Feb 16;18(2):260-74
references.pmid: 20159596
references.citation: Mech Dev. 1995 Jan;49(1-2):133-58
references.pmid: 7748785
references.citation: Proc Natl Acad Sci U S A. 1984 May;81(10):3088-92
references.pmid: 6587342
references.citation: J Theor Biol. 1979 Dec 7;81(3):389-400
references.pmid: 537379
references.citation: Biochem Biophys Res Commun. 1964 Jun 1;16(2):174-81
references.pmid: 4224521
references.citation: Int J Dev Biol. 2006;50(2-3):103-11
references.pmid: 16479479
references.citation: Science. 1976 Sep 10;193(4257):969-81
references.pmid: 948762
references.citation: J Theor Biol. 1969 Oct;25(1):1-47
references.pmid: 4390734
references.citation: Proc Natl Acad Sci U S A. 2010 Jun 1;107(22):10092-6
references.pmid: 20479267
references.citation: Proc Natl Acad Sci U S A. 2005 Dec 20;102(51):18403-7
references.pmid: 16352710
references.citation: Nature. 2004 Jul 15;430(6997):368-71
references.pmid: 15254541
references.citation: Development. 2000 Jan;127(2):279-89
references.pmid: 10603346
references.citation: Dev Biol. 2008 Apr 15;316(2):350-8
references.pmid: 18328473
references.citation: Nature. 1980 Oct 30;287(5785):795-801
references.pmid: 6776413
references.citation: Genes Dev. 1987 Oct;1(8):868-79
references.pmid: 3123323
references.citation: Curr Biol. 2008 Jul 22;18(14):1055-61
references.pmid: 18639459
references.citation: Nat Rev Neurosci. 2004 Jun;5(6):502-10
references.pmid: 15152200
references.citation: Dev Genes Evol. 2005 Jul;215(7):374-81
references.pmid: 15834586
references.citation: Development. 2009 Feb;136(4):605-14
references.pmid: 19168676
references.citation: Philos Trans R Soc Lond B Biol Sci. 2015 Apr 19;370(1666):
references.pmid: 25750229
references.citation: PLoS Biol. 2009 Mar;7(3):e1000049
references.pmid: 19750121
references.citation: Dev Cell. 2005 Jun;8(6):915-24
references.pmid: 15935780
references.citation: J Phys Chem A. 2011 Apr 14;115(14):2994-8
references.pmid: 21428383
references.citation: Dev Biol. 2004 Jul 1;271(1):38-48
references.pmid: 15196948
references.citation: Cell. 1988 Jul 1;54(1):83-93
references.pmid: 3383244
references.citation: Development. 1989;107 Suppl:13-9
references.pmid: 2483989
references.citation: Cell. 2006 Oct 6;127(1):27-32
references.pmid: 17018270
references.citation: Proc Natl Acad Sci U S A. 1922 Jun;8(6):151-4
references.pmid: 16576643
references.citation: Nature. 1994 Nov 10;372(6502):132-3
references.pmid: 7969442
references.citation: PLoS Comput Biol. 2006 May;2(5):e51
references.pmid: 16710449
references.citation: Bioinformatics. 2009 Feb 1;25(3):346-52
references.pmid: 19052059
references.citation: Nature. 2002 Sep 19;419(6904):261-2
references.pmid: 12239551
references.citation: Cell tissue biol. 2008 Apr;2(2):200-215
references.pmid: 19343098
references.citation: Phys Rev Lett. 1990 Jun 11;64(24):2953-2956
references.pmid: 10041855
references.citation: Cold Spring Harb Perspect Biol. 2009 Aug;1(2):a001891
references.pmid: 20066085
references.citation: Nature. 2005 Sep 8;437(7056):231-4
references.pmid: 16148928
references.citation: Nature. 1970 Jan 31;225(5231):420-2
references.pmid: 5411117
references.citation: Cell. 2007 Jul 13;130(1):153-64
references.pmid: 17632062
references.citation: Curr Biol. 2005 Nov 8;15(21):R887-99
references.pmid: 16271864
references.citation: Development. 2006 Jan;133(2):183-93
references.pmid: 16368928
references.citation: Curr Top Dev Biol. 1991;25:17-43
references.pmid: 1743055
references.citation: Bioessays. 2000 Nov;22(11):1048
references.pmid: 11056483
references.citation: PLoS One. 2011 Apr 22;6(4):e19122
references.pmid: 21544208
references.citation: Dev Biol. 1983 Apr;96(2):375-85
references.pmid: 6832478
references.citation: J Embryol Exp Morphol. 1973 Feb;29(1):27-38
references.pmid: 4722156
references.citation: Science. 1972 Feb 11;175(4022):634-6
references.pmid: 17808803
references.citation: Cold Spring Harb Perspect Biol. 2009 Jul;1(1):a000463
references.pmid: 20066073
references.citation: Development. 2010 Jul;137(14):2253-64
references.pmid: 20570935
references.citation: Development. 1993 Apr;117(4):1385-96
references.pmid: 8404539
references.citation: Nature. 2005 Mar 10;434(7030):229-34
references.pmid: 15759004
references.citation: Development. 1996 Apr;122(4):1281-9
references.pmid: 8620855
references.citation: Cell. 2005 Mar 25;120(6):873-86
references.pmid: 15797386
references.citation: Cell. 1993 Oct 8;75(1):165-74
references.pmid: 7691414
references.citation: Nat Cell Biol. 2011 Jan;13(1):22-9
references.pmid: 21170036
references.citation: Proc Natl Acad Sci U S A. 2009 Apr 21;106(16):6837-42
references.pmid: 19351900
references.citation: Cell. 1991 May 31;65(5):725-35
references.pmid: 1904007
references.citation: Proc Natl Acad Sci U S A. 2008 Feb 26;105(8):2901-6
references.pmid: 18287046
references.citation: Biophys J. 2010 Aug 9;99(4):L33-5
references.pmid: 20712981
references.citation: Proc Natl Acad Sci U S A. 2009 Feb 10;106(6):1710-5
references.pmid: 19190186
references.citation: Wilehm Roux Arch Dev Biol. 1977 Sep;183(3):249-268
references.pmid: 28305090
references.citation: Proc Natl Acad Sci U S A. 2001 Dec 4;98(25):14202-7
references.pmid: 11734639
references.citation: Development. 1994 Aug;120(8):2245-57
references.pmid: 7925025
references.citation: Nature. 1969 Aug 30;223(5209):913-6
references.pmid: 5803393
references.citation: Genetics. 1991 Dec;129(4):1119-36
references.pmid: 1783295
references.citation: Mol Cell Biol. 1998 May;18(5):2892-900
references.pmid: 9566908
references.citation: Cell. 1993 Jul 30;74(2):347-55
references.pmid: 8343961
references.citation: J Theor Biol. 1980 Aug 7;85(3):429-50
references.pmid: 7442273
references.citation: Cell. 1985 Oct;42(3):791-8
references.pmid: 3931919
references.citation: Kybernetik. 1964 Jun;2(2):43-61
references.pmid: 5833193
references.citation: Proc Natl Acad Sci U S A. 2007 May 15;104 Suppl 1:8597-604
references.pmid: 17494740
references.citation: Science. 2009 May 8;324(5928):772-5
references.pmid: 19423823
references.citation: Nat New Biol. 1972 Sep 27;239(91):98-101
references.pmid: 4507522
references.citation: EMBO J. 2001 Apr 2;20(7):1563-72
references.pmid: 11285221
references.citation: Nat Rev Mol Cell Biol. 2008 Mar;9(3):255-62
references.pmid: 18292780
references.citation: Nature. 2000 Jul 13;406(6792):188-92
references.pmid: 10910359
references.citation: Proc Natl Acad Sci U S A. 1920 Jul;6(7):410-5
references.pmid: 16576509
references.citation: Curr Biol. 2010 Mar 9;20(5):R249-54
references.pmid: 20219179
references.citation: J Embryol Exp Morphol. 1973 Feb;29(1):39-52
references.pmid: 4722157
references.citation: PLoS Biol. 2011 Mar;9(3):e1000596
references.pmid: 21390295
references.citation: J Theor Biol. 1969 Oct;25(1):49-107
references.pmid: 4390735
references.citation: Experientia. 1946 Nov 15;2(11):451-3
references.pmid: 20340479
references.citation: Development. 2011 Jul;138(13):2741-9
references.pmid: 21613328
references.citation: Proc Natl Acad Sci U S A. 2006 Aug 1;103(31):11613-8
references.pmid: 16864795
references.citation: Cell. 1992 Jan 24;68(2):201-19
references.pmid: 1733499