title: On the biophysics and kinetics of toehold-mediated DNA strand displacement.
abstract: Dynamic DNA nanotechnology often uses toehold-mediated strand displacement for controlling reaction kinetics. Although the dependence of strand displacement kinetics on toehold length has been experimentally characterized and phenomenologically modeled, detailed biophysical understanding has remained elusive. Here, we study strand displacement at multiple levels of detail, using an intuitive model of a random walk on a 1D energy landscape, a secondary structure kinetics model with single base-pair steps and a coarse-grained molecular model that incorporates 3D geometric and steric effects. Further, we experimentally investigate the thermodynamics of three-way branch migration. Two factors explain the dependence of strand displacement kinetics on toehold length: (i) the physical process by which a single step of branch migration occurs is significantly slower than the fraying of a single base pair and (ii) initiating branch migration incurs a thermodynamic penalty, not captured by state-of-the-art nearest neighbor models of DNA, due to the additional overhang it engenders at the junction. Our findings are consistent with previously measured or inferred rates for hybridization, fraying and branch migration, and they provide a biophysical explanation of strand displacement kinetics. Our work paves the way for accurate modeling of strand displacement cascades, which would facilitate the simulation and construction of more complex molecular systems.
authors.affiliation: Computation and Neural Systems, California Institute of Technology, Pasadena, CA 91125, USA, Rudolph Peierls Centre for Theoretical Physics, Department of Physics, University of Oxford, Oxford OX1 3NP, UK, Computer Science, California Institute of Technology, Pasadena, CA 91125, USA, Departments of Electrical and Computer Engineering, Materials Science and Engineering, Boise State University, ID83725, USA, Physical and Theoretical Chemistry Laboratory, Department of Chemistry, University of Oxford, Oxford OX1 3QZ, UK and Bioengineering, California Institute of Technology, Pasadena, CA 91125, USA.
authors.forename: Niranjan
authors.initials: N
authors.lastname: Srinivas
authors.forename: Thomas E
authors.initials: TE
authors.lastname: Ouldridge
authors.forename: Petr
authors.initials: P
authors.lastname: Sulc
authors.forename: Joseph M
authors.initials: JM
authors.lastname: Schaeffer
authors.forename: Bernard
authors.initials: B
authors.lastname: Yurke
authors.forename: Ard A
authors.initials: AA
authors.lastname: Louis
authors.forename: Jonathan P K
authors.initials: JP
authors.lastname: Doye
authors.forename: Erik
authors.initials: E
authors.lastname: Winfree
mesh_terms: D000465:Algorithms; D055592:Biophysical Phenomena; D004247:DNA / Q000737:chemistry*; D007700:Kinetics; D008958:Models, Molecular; D013816:Thermodynamics
chemical_list: D004247:DNA
references.citation: Annu Rev Biophys Biomol Struct. 2004;33:415-40
references.pmid: 15139820
references.citation: Nat Biotechnol. 2005 Nov;23(11):1424-33
references.pmid: 16244657
references.citation: ACS Nano. 2013 Mar 26;7(3):2479-90
references.pmid: 23414564
references.citation: Mol Biol Biochem Biophys. 1977;24:191-218
references.pmid: 904614
references.citation: J Am Chem Soc. 2011 Feb 23;133(7):2177-82
references.pmid: 21268641
references.citation: Annu Rev Biophys Bioeng. 1976;5:337-61
references.pmid: 7992
references.citation: J Chem Phys. 2011 Feb 28;134(8):085101
references.pmid: 21361556
references.citation: Phys Rev Lett. 2010 Apr 30;104(17):178101
references.pmid: 20482144
references.citation: Proc Natl Acad Sci U S A. 1994 Mar 15;91(6):2021-5
references.pmid: 8134343
references.citation: J Mol Biol. 2000 Mar 24;297(2):511-20
references.pmid: 10715217
references.citation: Soft Matter. 2009 Mar 21;5(6):1251-1262
references.pmid: 23227104
references.citation: J Chem Phys. 2009 Jun 21;130(23):234101
references.pmid: 19548705
references.citation: J Comput Chem. 2011 Jan 15;32(1):170-3
references.pmid: 20645303
references.citation: Methods Enzymol. 1989;180:304-25
references.pmid: 2482421
references.citation: Phys Rev Lett. 1988 Dec 5;61(23):2635-2638
references.pmid: 10039183
references.citation: Annu Rev Biophys Biophys Chem. 1988;17:265-86
references.pmid: 3293588
references.citation: Nature. 2008 Mar 13;452(7184):198-201
references.pmid: 18337818
references.citation: J Mol Biol. 1977 Nov;116(4):825-39
references.pmid: 592403
references.citation: Clin Chem. 2001 Nov;47(11):1956-61
references.pmid: 11673362
references.citation: Proc Natl Acad Sci U S A. 2004 Oct 26;101(43):15275-8
references.pmid: 15492210
references.citation: J Am Chem Soc. 2005 May 18;127(19):6914-5
references.pmid: 15884910
references.citation: Nucleic Acids Res. 2006 Jul 05;34(11):3370-7
references.pmid: 16822858
references.citation: Proc Natl Acad Sci U S A. 1994 Sep 27;91(20):9218-22
references.pmid: 7524072
references.citation: Biochemistry. 2008 May 13;47(19):5336-53
references.pmid: 18422348
references.citation: Proc Natl Acad Sci U S A. 2004 May 11;101(19):7287-92
references.pmid: 15123812
references.citation: Science. 2007 Nov 16;318(5853):1121-5
references.pmid: 18006742
references.citation: Nat Biotechnol. 2010 Nov;28(11):1208-12
references.pmid: 21037591
references.citation: Nat Chem. 2011 Feb;3(2):103-13
references.pmid: 21258382
references.citation: Nucleic Acids Res. 2003 Jul 1;31(13):3429-31
references.pmid: 12824340
references.citation: J Am Chem Soc. 2006 Oct 4;128(39):12693-9
references.pmid: 17002363
references.citation: Proc Natl Acad Sci U S A. 2010 Sep 7;107(36):15898-903
references.pmid: 20713708
references.citation: J Mol Biol. 1999 May 21;288(5):911-40
references.pmid: 10329189
references.citation: Nucleic Acids Res. 2003 Jul 1;31(13):3406-15
references.pmid: 12824337
references.citation: Nucleic Acids Res. 2001 Jun 1;29(11):2303-13
references.pmid: 11376149
references.citation: Nucleic Acids Res. 2013 Oct;41(19):8886-95
references.pmid: 23935069
references.citation: J Chem Phys. 2007 Oct 21;127(15):154101
references.pmid: 17949126
references.citation: Nucleic Acids Res. 2010 Jul;38(12):4182-97
references.pmid: 20194118
references.citation: J Mol Biol. 2004 Sep 17;342(3):775-85
references.pmid: 15342236
references.citation: J Mol Biol. 1968 Feb 14;31(3):349-70
references.pmid: 5637197
references.citation: J Chem Phys. 2013 Feb 28;138(8):085101
references.pmid: 23464177
references.citation: J Mol Biol. 1971 Dec 14;62(2):383-401
references.pmid: 5138338
references.citation: Nucleic Acids Res. 1981 Apr 24;9(8):1905-18
references.pmid: 6264399
references.citation: Nature. 2006 Mar 16;440(7082):297-302
references.pmid: 16541064
references.citation: Science. 2011 Jun 3;332(6034):1196-201
references.pmid: 21636773
references.citation: Mol Biotechnol. 2007 Nov;37(3):246-57
references.pmid: 17952671
references.citation: Biophys Chem. 1974 Aug;2(2):83-96
references.pmid: 4433687
references.citation: Proc Natl Acad Sci U S A. 1998 Feb 17;95(4):1460-5
references.pmid: 9465037
references.citation: Nucleic Acids Res. 2006 Jan 31;34(2):564-74
references.pmid: 16449200
references.citation: Science. 2006 Dec 8;314(5805):1585-8
references.pmid: 17158324
references.citation: Biochemistry. 1992 Dec 8;31(48):12055-61
references.pmid: 1280997
references.citation: Phys Rev Lett. 2005 Jan 14;94(1):018104
references.pmid: 15698138
references.citation: Biophys Chem. 1974 Aug;2(2):97-101
references.pmid: 4433688
references.citation: Nat Nanotechnol. 2011 Nov 06;6(12):763-72
references.pmid: 22056726
references.citation: Nature. 2000 Aug 10;406(6796):605-8
references.pmid: 10949296
references.citation: Nature. 2008 Jan 17;451(7176):318-22
references.pmid: 18202654
references.citation: Nat Nanotechnol. 2007 May;2(5):275-84
references.pmid: 18654284
references.citation: Biochemistry. 1993 Mar 30;32(12):3095-104
references.pmid: 8457571
references.citation: J Chem Phys. 2012 Jun 7;136(21):215102
references.pmid: 22697570
references.citation: Angew Chem Int Ed Engl. 2011 Mar 28;50(14):3124-56
references.pmid: 21432950
references.citation: J Am Chem Soc. 2012 Jan 11;134(1):263-71
references.pmid: 22129141
references.citation: Phys Rev Lett. 2008 Dec 5;101(23):238101
references.pmid: 19113596
references.citation: J Am Chem Soc. 2009 Dec 2;131(47):17303-14
references.pmid: 19894722
references.citation: J Am Chem Soc. 2002 Feb 13;124(6):1097-103
references.pmid: 11829619
references.citation: Nucleic Acids Res. 1996 Nov 15;24(22):4395-400
references.pmid: 8948629
references.citation: Biochemistry. 1996 Mar 19;35(11):3555-62
references.pmid: 8639506
references.citation: RNA. 2000 Mar;6(3):325-38
references.pmid: 10744018
references.citation: Nature. 2012 May 30;485(7400):623-6
references.pmid: 22660323
references.citation: J Mol Biol. 2004 Aug 13;341(3):739-51
references.pmid: 15288783
references.citation: J Phys Condens Matter. 2009 Nov 18;21(46):463102
references.pmid: 21715864
references.citation: Nature. 1998 Aug 6;394(6693):539-44
references.pmid: 9707114
references.citation: Nucleic Acids Res. 2000 May 1;28(9):1929-34
references.pmid: 10756193
references.citation: Biochemistry. 1981 Mar 17;20(6):1409-13
references.pmid: 6261793
references.citation: Curr Opin Struct Biol. 2013 Apr;23(2):206-11
references.pmid: 23305848
references.citation: Nucleic Acids Res. 2003 Feb 15;31(4):1319-30
references.pmid: 12582252
references.citation: Proc Natl Acad Sci U S A. 2010 Mar 23;107(12):5393-8
references.pmid: 20203007