title: Protein structural modularity and robustness are associated with evolvability.
abstract: Theory suggests that biological modularity and robustness allow for maintenance of fitness under mutational change, and when this change is adaptive, for evolvability. Empirical demonstrations that these traits promote evolvability in nature remain scant however. This is in part because modularity, robustness, and evolvability are difficult to define and measure in real biological systems. Here, we address whether structural modularity and/or robustness confer evolvability at the level of proteins by looking for associations between indices of protein structural modularity, structural robustness, and evolvability. We propose a novel index for protein structural modularity: the number of regular secondary structure elements (helices and strands) divided by the number of residues in the structure. We index protein evolvability as the proportion of sites with evidence of being under positive selection multiplied by the average rate of adaptive evolution at these sites, and we measure this as an average over a phylogeny of 25 mammalian species. We use contact density as an index of protein designability, and thus, structural robustness. We find that protein evolvability is positively associated with structural modularity as well as structural robustness and that the effect of structural modularity on evolvability is independent of the structural robustness index. We interpret these associations to be the result of reduced constraints on amino acid substitutions in highly modular and robust protein structures, which results in faster adaptation through natural selection.
authors: Department of Genetics, Yale University, New Haven, Connecticut, USA. mmrorick@gmail.com
authors: Mary M
authors: MM
authors: Rorick
authors: Günter P
authors: GP
authors: Wagner
references: Genome Res. 2005 Mar;15(3):385-92
references: 15741509
references: Nat Rev Genet. 2008 Jan;9(1):75-82
references: 18059367
references: Science. 2002 Apr 26;296(5568):750-2
references: 11976460
references: J Exp Zool B Mol Dev Evol. 2008 May 15;310(3):216-26
references: 17973270
references: Evolution. 1996 Jun;50(3):967-976
references: 28565291
references: Evol Dev. 2006 Jan-Feb;8(1):94-100
references: 16409386
references: Bioessays. 2000 Apr;22(4):372-80
references: 10723034
references: BMC Bioinformatics. 2007 Jul 03;8:237
references: 17608939
references: Mol Biol Evol. 2005 Apr;22(4):1147-55
references: 15689524
references: FEBS Lett. 2002 Feb 20;513(1):129-34
references: 11911892
references: Science. 1996 Aug 2;273(5275):666-9
references: 8662562
references: HFSP J. 2007 May;1(1):79-87
references: 19404462
references: Biosystems. 2003 May;69(2-3):83-94
references: 12689723
references: Evolution. 1997 Apr;51(2):329-347
references: 28565347
references: Evolution. 2003 Sep;57(9):1959-72
references: 14575319
references: Biophys J. 2005 Dec;89(6):3714-20
references: 16150971
references: Mol Biol Evol. 2000 Feb;17(2):301-8
references: 10677853
references: Protein Sci. 1999 Feb;8(2):370-80
references: 10048330
references: Proc Natl Acad Sci U S A. 1999 Mar 16;96(6):2591-5
references: 10077554
references: BMC Bioinformatics. 2006 Sep 05;7:402
references: 16953874
references: Bioinformatics. 2009 Jan 15;25(2):288-9
references: 19033274
references: Evolution. 2003 Jun;57(6):1448-50
references: 12894952
references: Proc Biol Sci. 2010 May 7;277(1686):1403-8
references: 20053642
references: Evolution. 2002 Aug;56(8):1549-56
references: 12353747
references: Mol Biol Evol. 2007 Apr;24(4):1005-11
references: 17264066
references: Proc Biol Sci. 2006 Feb 22;273(1585):457-64
references: 16615213
references: Proc Natl Acad Sci U S A. 2003 Jul 22;100(15):8727-31
references: 12843403
references: Proteins. 1997 Dec;29(4):461-6
references: 9408943
references: Genome Biol Evol. 2010 Jul 12;2:166-79
references: 20624723
references: PLoS Comput Biol. 2008 Jul 18;4(7):e1000110
references: 18636097
references: Nucleic Acids Res. 2005 Jan 1;33(Database issue):D178-82
references: 15608172
references: Proc Biol Sci. 2008 Jul 22;275(1643):1595-602
references: 18430649
references: J Proteome Res. 2007 Oct;6(10):3924-34
references: 17850063
references: Mol Biol Evol. 2006 Feb;23(2):327-37
references: 16237209
references: Bioessays. 2002 Dec;24(12):1164-77
references: 12447981
references: Mol Biol Evol. 2006 Nov;23(11):2072-80
references: 16887903
references: Mol Biol Evol. 2007 Aug;24(8):1586-91
references: 17483113
references: Annu Rev Biochem. 2006;75:655-80
references: 16756506
references: Nat Genet. 2000 May;25(1):25-9
references: 10802651
references: Proc Natl Acad Sci U S A. 2002 Jan 22;99(2):809-14
references: 11805332
references: J Theor Biol. 2001 Sep 7;212(1):35-46
references: 11527443
references: BMC Evol Biol. 2003 Oct 02;3:21
references: 14525624
references: Proc Biol Sci. 2008 Jan 7;275(1630):91-100
references: 17971325
references: J Mol Biol. 1999 Oct 22;293(2):321-31
references: 10550212
references: BMC Syst Biol. 2007 Jun 04;1:24
references: 17547772
references: Proc Natl Acad Sci U S A. 2005 Oct 4;102(40):14338-43
references: 16176987
references: Nat Rev Genet. 2004 Nov;5(11):826-37
references: 15520792
references: Trends Genet. 2006 Aug;22(8):416-9
references: 16797778
references: Mol Biol Evol. 2006 Sep;23(9):1751-61
references: 16782762
references: Trends Biotechnol. 2005 Oct;23(10):485-7
references: 16054255
references: Curr Opin Struct Biol. 2009 Jun;19(3):335-40
references: 19386484
references: Nat Rev Genet. 2007 Dec;8(12):921-31
references: 18007649
references: Proc Natl Acad Sci U S A. 2008 Sep 9;105(36):13292-7
references: 18757736
references: BMC Evol Biol. 2002 Nov 1;2:20
references: 12410938
references: BMC Evol Biol. 2007 Nov 30;7:241
references: 18053139
references: Bioessays. 2000 Nov;22(11):1043-5
references: 11056481
references: PLoS Comput Biol. 2007 Dec;3(12):e239
references: 18069884
references: BMC Evol Biol. 2004 Jun 01;4:14
references: 15171796
references: Genetics. 2005 May;170(1):433-46
references: 15781713
references: Nature. 1999 Dec 2;402(6761 Suppl):C47-52
references: 10591225
references: Biosystems. 2007 Sep-Oct;90(2):475-85
references: 17276586
references: Comput Appl Biosci. 1997 Oct;13(5):555-6
references: 9367129
references: Proc Natl Acad Sci U S A. 2002 Aug 6;99(16):10382-7
references: 12149452
references: Mol Biochem Parasitol. 2006 Jul;148(1):1-9
references: 16621067
references: Biopolymers. 2000 Jan;53(1):1-8
references: 10644946
references: Life Sci. 2009 Feb 13;84(7-8):189-93
references: 19109982
references: Evol Dev. 2001 Mar-Apr;3(2):59-72
references: 11341675
references: Biopolymers. 1983 Dec;22(12):2577-637
references: 6667333
references: Philos Trans R Soc Lond B Biol Sci. 2006 Mar 29;361(1467):507-17
references: 16524839
references: BMC Bioinformatics. 2010 Apr 26;11:204
references: 20420672
references: Nat Biotechnol. 2007 Sep;25(9):1051-6
references: 17721510
references: Protein Eng Des Sel. 2005 Feb;18(2):59-64
references: 15788422
references: J Theor Biol. 1996 Oct 7;182(3):303-9
references: 8944162
references: Evol Dev. 2003 Mar-Apr;5(2):169-79
references: 12622734
references: Proc Natl Acad Sci U S A. 2007 May 15;104 Suppl 1:8597-604
references: 17494740
references: Mol Biol Evol. 2004 Jan;21(1):108-16
references: 14595100
references: Nature. 2010 Jan 21;463(7279):353-5
references: 20090752
references: J Mol Evol. 2002 Jul;55(1):104-10
references: 12165847
references: J Exp Zool. 2000 Oct 15;288(3):242-83
references: 11069142
references: BMC Struct Biol. 2008 Mar 07;8:15
references: 18325123
references: Proteins. 2007 Mar 1;66(4):761-5
references: 17154416
references: Phys Rev Lett. 2003 May 30;90(21):218101
references: 12786593
references: Evol Dev. 2006 Jan-Feb;8(1):81-93
references: 16409385
references: BMC Bioinformatics. 2010 Feb 04;11:75
references: 20132552
references: Proc Natl Acad Sci U S A. 2005 Jan 18;102(3):606-11
references: 15644440