Beyond the French Flag Model: Exploiting Spatial and Gene Regulatory Interactions for Positional Information.
A crucial step in the early development of multicellular organisms involves the establishment of spatial patterns of gene expression which later direct proliferating cells to take on different cell fates. These patterns enable the cells to infer their global position within a tissue or an organism by reading out local gene expression levels. The patterning system is thus said to encode positional information, a concept that was formalized recently in the framework of information theory. Here we introduce a toy model of patterning in one spatial dimension, which can be seen as an extension of Wolpert's paradigmatic "French Flag" model, to patterning by several interacting, spatially coupled genes subject to intrinsic and extrinsic noise. Our model, a variant of an Ising spin system, allows us to systematically explore expression patterns that optimally encode positional information. We find that optimal patterning systems use positional cues, as in the French Flag model, together with gene-gene interactions to generate combinatorial codes for position which we call "Counter" patterns. Counter patterns can also be stabilized against noise and variations in system size or morphogen dosage by longer-range spatial interactions of the type invoked in the Turing model. The simple setup proposed here qualitatively captures many of the experimentally observed properties of biological patterning systems and allows them to be studied in a single, theoretically consistent framework.
Physics of Complex Biosystems, Physics Department,Technical University of Munich, James-Franck-Str. 1, D-85748 Garching, Germany.
Patrick
P
Hillenbrand
Physics of Complex Biosystems, Physics Department,Technical University of Munich, James-Franck-Str. 1, D-85748 Garching, Germany.
Ulrich
U
Gerland
Institute of Science and Technology Austria, Am Campus 1, A-3400 Klosterneuburg, Austria.
Gašper
G
Tkačik
Proc Natl Acad Sci U S A. 2007 Jun 26;104(26):10926-31
17569783
Science. 2014 Aug 1;345(6196):566-70
25082703
Proc Natl Acad Sci U S A. 2008 Aug 26;105(34):12265-70
18719112
Nature. 2006 Apr 20;440(7087):1007-12
16625187
Cell. 1988 Jul 1;54(1):95-104
3383245
Development. 2015 Feb 1;142(3):587-96
25605785
Phys Rev E. 2016 Feb;93(2):022404
26986359
Phys Rev Lett. 2009 Dec 18;103(25):258101
20366291
PLoS Comput Biol. 2009 Mar;5(3):e1000303
19282965
Curr Opin Biotechnol. 2014 Aug;28:149-55
24846821
PLoS One. 2007 Oct 24;2(10):e1077
17957259
Science. 2012 Dec 14;338(6113):1476-80
23239739
Proc Natl Acad Sci U S A. 2002 Oct 1;99(20):12795-800
12237400
Development. 2000 Apr;127(7):1337-48
10704381
Cell. 2007 Jul 13;130(1):153-64
17632062
Development. 2014 Jan;141(2):318-24
24306107
Phys Rev Lett. 2009 May 29;102(21):218101
19519137
PLoS Biol. 2009 Mar;7(3):e1000049
19750121
Phys Rev E Stat Nonlin Soft Matter Phys. 2010 Apr;81(4 Pt 1):041905
20481751
Nat Rev Genet. 2011 Jan;12(1):43-55
21164524
J Theor Biol. 1969 Oct;25(1):1-47
4390734
Nat Rev Mol Cell Biol. 2006 Jan;7(1):45-53
16493412
Nature. 2004 Jul 15;430(6997):368-71
15254541
Cell. 1997 Nov 28;91(5):639-48
9393857
Phys Rev E Stat Nonlin Soft Matter Phys. 2012 Apr;85(4 Pt 1):041903
22680494
Development. 1989;107 Suppl:3-12
2699855
Science. 2010 May 21;328(5981):1021-5
20413456
PLoS One. 2008 Jul 23;3(7):e2774
18648612
Dev Dyn. 2006 Nov;235(11):2949-60
16960857
Development. 2008 Oct;135(19):3175-83
18776142
Proc Natl Acad Sci U S A. 2013 Oct 8;110(41):16301-8
24089448
J Theor Biol. 1976 May 21;58(2):455-76
940335
Mol Biosyst. 2009 Dec;5(12):1549-68
20023719
Phys Rev E Stat Nonlin Soft Matter Phys. 2009 Sep;80(3 Pt 1):031920
19905159
Genetics. 2015 Jan;199(1):39-59
25361898
Nature. 1995 Jun 29;375(6534):787-90
7596411
Development. 2012 Feb;139(4):625-39
22274695
Nat Rev Mol Cell Biol. 2006 Sep;7(9):678-89
16921404
Science. 2014 Dec 12;346(6215):1370-3
25504722
Phys Rev E Stat Nonlin Soft Matter Phys. 2015 Jun;91(6):062710
26172739
Development. 2008 Mar;135(6):1137-46
18296653
Elife. 2015 May 18;4:null
25985085
Bioessays. 2006 Nov;28(11):1102-11
17041900
BMC Dev Biol. 2010 Aug 02;10:80
20678215
Nature. 2004 Jan 29;427(6973):415-8
14749823
Science. 2011 Oct 21;334(6054):354-8
21921160
Cell. 2007 Jul 27;130(2):205-9
17662932
Phys Rev E Stat Nonlin Soft Matter Phys. 2008 Jul;78(1 Pt 1):011910
18763985
Proc Natl Acad Sci U S A. 2013 Apr 23;110(17):6724-9
23580621
J Physiol. 2014 Jun 1;592(11):2267-81
24882812
Cell. 1991 Mar 22;64(6):1083-92
2004417
Curr Biol. 2005 Nov 8;15(21):1888-98
16271865