Deoxyribonucleic acid (DNA) is an essential molecule that enables the storage and retrieval of genetic information. In its role during cellular processes, this long flexible molecule is significantly bent and twisted. Previously, we developed an elastodynamic rod approximation to study DNA deformed into a loop by a gene regulatory protein (lac repressor) and predicted the energetics and topology of the loops. Although adequate for DNA looping, our model neglected electrostatic interactions, which are essential when considering processes that result in highly supercoiled DNA including plectonemes. Herein, we extend the rod approximation to account for electrostatic interactions and present strategies that improve computational efficiency. Our calculations for the stability for a circularly bent rod and for an initially straight rod compare favorably to existing equilibrium models. With this new capability, we are now well-positioned to study the dynamics of transcription and other dynamic processes that result in DNA supercoiling.
Issue Section:
Research Papers
1.
Watson
, J. D.
, and Crick
, F. H. C.
, 1953, “Molecular Structure of Nucleic Acids—A Structure for Deoxyribose Nucleic Acid
,” Nature (London)
0028-0836, 171
(4356
), pp. 737
–738
.2.
Franklin
, R. E.
, and Gosling
, R. G.
, 1953, “Molecular Configuration in Sodium Thymonucleate
,” Nature (London)
0028-0836, 171
(4356
), pp. 740
–741
.3.
Calladine
, C. R.
, Drew
, H. R.
, Luisi
, B. F.
, and Travers
, A. A.
, 2004. Understanding DNA: The Molecule and How It Works
, 3rd ed., Elsevier Academic Press
, San Diego, CA
.4.
Fuller
, F. B.
, 1971, “The Writhing Number of a Space Curve
,” Proc. Natl. Acad. Sci. U.S.A.
0027-8424, 68
(4
), pp. 815
–819
.5.
Lankaš
, F.
, Lavery
, R.
, and Maddocks
, J. H.
, 2006, “Kinking Occurs During Molecular Dynamics Simulations of Small DNA Minicircles
,” Structure (London)
0969-2126, 14
(10
), pp. 1527
–1534
.6.
Beveridge
, D. L.
, Barreiro
, G.
, Byun
, K. S.
, Case
, D. A.
, Cheatham
, T. E.
, Dixit
, S. B.
, Giudice
, E.
, Lankas
, F.
, Lavery
, R.
, Maddocks
, J. H.
, Osman
, R.
, Seibert
, E.
, Sklenar
, H.
, Stoll
, G.
, Thayer
, K. M.
, Varnai
, P.
, and Young
, M. A.
, 2004, “Molecular Dynamics Simulations of the 136 Unique Tetranucleotide Sequences of DNA Oligonucleotides. I. Research Design and Results on d(C(p)G) Steps
,” Biophys. J.
0006-3495, 87
(6
), pp. 3799
–3813
.7.
Dans
, P. D.
, Zeida
, A.
, Machado
, M. R.
, and Pantano
, S.
, 2010, “A Coarse Grained Model for Atomic-Detailed DNA Simulations With Explicit Electrostatics
,” J. Chem. Theory Comput.
1549-9618, 6
(5
), pp. 1711
–1725
.8.
Morriss-Andrews
, A.
, Rottler
, J.
, and Plotkin
, S. S.
, 2010, “A Systematically Coarse-Grained Model for DNA and Its Predictions for Persistence Length, Stacking, Twist, and Chirality
,” J. Chem. Phys.
0021-9606, 132
(3
), p. 035105
.9.
Goyal
, S.
, Perkins
, N. C.
, and Lee
, C. L.
, 2005, “Nonlinear Dynamics and Loop Formation in Kirchhoff Rods With Implications to the Mechanics of DNA and Cables
,” J. Comput. Phys.
0021-9991, 209
(1
), pp. 371
–389
.10.
Goyal
, S.
, Lillian
, T.
, Blumberg
, S.
, Meiners
, J. -C.
, Meyhöfer
, E.
, and Perkins
, N. C.
, 2007, “Intrinsic Curvature of DNA Influences LacR-Mediated Looping
,” Biophys. J.
0006-3495, 93
(12
), pp. 4342
–4359
.11.
Lillian
, T. D.
, Goyal
, S.
, Kahn
, J. D.
, Meyhöfer
, E.
, and Perkins
, N. C.
, 2008, “Computational Analysis of Looping of a Large Family of Highly Bent DNA by LacI
,” Biophys. J.
0006-3495, 95
(12
), pp. 5832
–5842
.12.
Lillian
, T. D.
, Perkins
, N. C.
, and Goyal
, S.
, 2008, “Computational Elastic Rod Model Applied to DNA Looping
,” Proceedings of ASME IDETC/CIE 2007
, Las Vegas, NV, Sep. 4–7, Vol. 5
, pp. 1449
–1456
.13.
Goyal
, S.
, 2006, “A Dynamic Rod Model to Simulate Mechanics of Cables and DNA
,” Ph.D. thesis, University of Michigan.14.
Strick
, T.
, Allemand
, J. F.
, Croquette
, V.
, and Bensimon
, D.
, 2000, “Twisting and Stretching Single DNA Molecules
,” Prog. Biophys. Mol. Biol.
0079-6107, 74
(1–2
), pp. 115
–140
.15.
Bustamante
, C.
, Marko
, J. F.
, Siggia
, E. D.
, and Smith
, S.
, 1994, “Entropic Elasticity of Lambda-Phage DNA
,” Science
0036-8075, 265
(5178
), pp. 1599
–1600
.16.
Bryant
, Z.
, Stone
, M. D.
, Gore
, J.
, Smith
, S. B.
, Cozzarelli
, N. R.
, and Bustamante
, C.
, 2003, “Structural Transitions and Elasticity From Torque Measurements on DNA
,” Nature (London)
0028-0836, 424
(6946
), pp. 338
–341
.17.
Bustamante
, C.
, Bryant
, Z.
, and Smith
, S. B.
, 2003, “Ten Years of Tension: Single-Molecule DNA Mechanics
,” Nature (London)
0028-0836, 421
(6921
), pp. 423
–427
.18.
Manning
, R. S.
, Maddocks
, J. H.
, and Kahn
, J. D.
, 1996, “A Continuum Rod Model of Sequence-Dependent DNA Structure
,” J. Chem. Phys.
0021-9606, 105
(13
), pp. 5626
–5646
.19.
Swigon
, D.
, Coleman
, B. D.
, and Olson
, W. K.
, 2006, “Modeling the Lac Repressor-Operator Assembly: The Influence of DNA Looping on Lac Repressor conformation
,” Proc. Natl. Acad. Sci. U.S.A.
0027-8424, 103
(26
), pp. 9879
–9884
.20.
Munteanu
, M. G.
, Vlahovicek
, K.
, Parthasarathy
, S.
, Simon
, I.
, and Pongor
, S.
, 1998, “Rod Models of DNA: Sequence-Dependent Anisotropic Elastic Modelling of Local Bending Phenomena
,” Trends Biochem. Sci.
0167-7640, 23
(9
), pp. 341
–347
.21.
Schlick
, T.
, 1995, “Modeling Superhelical DNA: Recent Analytical and Dynamic Approaches
,” Curr. Opin. Struct. Biol.
0959-440X, 5
(2
), pp. 245
–262
.22.
Balaeff
, A.
, Mahadevan
, L.
, and Schulten
, K.
, 2006, “Modeling DNA Loops Using the Theory of Elasticity
,” Phys. Rev. E
1063-651X, 73
(3
), p. 031919
.23.
Baumann
, C. G.
, Smith
, S. B.
, Bloomfield
, V. A.
, and Bustamante
, C.
, 1997, “Ionic Effects on the Elasticity of Single DNA Molecules
,” Proc. Natl. Acad. Sci. U.S.A.
0027-8424, 94
(12
), pp. 6185
–6190
.24.
Strick
, T. R.
, Allemand
, J. F.
, Bensimon
, D.
, Bensimon
, A.
, and Croquette
, V.
, 1996, “The Elasticity of a Single Supercoiled DNA Molecule
,” Science
0036-8075, 271
(5257
), pp. 1835
–1837
.25.
Hagerman
, P. J.
, 1988, “Flexibility of DNA
,” Annu. Rev. Biophys. Biophys. Chem.
0883-9182, 17
, pp. 265
–286
.26.
Chung
, J.
, and Hulbert
, G. M.
, 1993, “A Time Integration Algorithm for Structural Dynamics With Improved Numerical Dissipation: The Generalized-Alpha Method
,” ASME J. Appl. Mech.
0021-8936, 60
(2
), pp. 371
–375
.27.
Vologodskii
, A.
, and Cozzarelli
, N.
, 1995, “Modeling of Long-Range Electrostatic Interactions in DNA
,” Biopolymers
0006-3525, 35
(3
), pp. 289
–296
.28.
Klapper
, I.
, 1996, “Biological Applications of the Dynamics of Twisted Elastic Rods
,” J. Comput. Phys.
0021-9991, 125
(2
), pp. 325
–337
.29.
Goyal
, S.
, Perkins
, N. C.
, and Lee
, C. L.
, 2008, “Non-Linear Dynamic Intertwining of Rods With Self-Contact
,” Int. J. Non-Linear Mech.
0020-7462, 43
(1
), pp. 65
–73
.30.
Delrow
, J. J.
, Gebe
, J. A.
, and Schurr
, J. M.
, 1997, “Comparison of Hard-Cylinder and Screened Coulomb Interactions in the Modeling of Supercoiled DNAs
,” Biopolymers
0006-3525, 42
(4
), pp. 455
–470
.31.
Coleman
, B. D.
, Swigon
, D.
, and Tobias
, I.
, 2000, “Elastic Stability of DNA Configurations. II. Supercoiled Plasmids With Self-Contact
,” Phys. Rev. E
1063-651X, 61
(1
), pp. 759
–770
.32.
van der Heijden
, G. H. M.
, Neukirch
, S.
, Goss
, V. G. A.
, and Thompson
, J. M. T.
, 2003, “Instability and Self-Contact Phenomena in the Writhing of Clamped Rods
,” Int. J. Mech. Sci.
0020-7403, 45
(1
), pp. 161
–196
.Copyright © 2011
by American Society of Mechanical Engineers
You do not currently have access to this content.
