Abstract
Due to the number of nucleotides in a typical system of interest, and the complexity of the interactions between them, it is impossible to find exact analytical expressions for the behaviour of a general coarse-grained model of DNA. Computer simulations can provide numerical information in the absence of any exact solutions, and guide the application of simpler, analytic descriptions.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
To avoid confusion, I shall take the term microstate to be a given set of positions, orientations, velocities and angular velocities for the system in question. The configuration is defined by the positions and orientation of entities in the sysem. Finally, I shall use the term state more broadly, to apply to a set of microstates or configurations which are in some way similar (for instance, the ‘duplex state’ consists of all microstates in which the two strands are bound to each other.
- 2.
The algorithm used is actually the variant detailed in the appendix of Ref. [9].
- 3.
Here I consider only additive noise, and can therefore neglect the subtleties of the distinction between Ito and Stratonovich calculus [12].
- 4.
Despite this reduction in noise, dynamics are still highly damped. For example, a simulation of a 10 bp duplex at 300 K initiated with all 10 bp formed but far from an optimal configuration (with around 70 % of the typical binding energy and no kinetic energy) will reach states typical of equilibrium in around \(10\) units of reduced time. For comparison, diffusion over its own length is around 10–100 times slower for a 10 bp duplex.
References
K. Huang. Statistical Mechanics, Second Edition. John Wiley and Sons, Inc., New York, 1987.
N. Metropolis et al. Equation of state calculation by fast computing machines. J. Chem. Phys., 21(6):1087–1092, 1953.
A. W. Wilber et al. Reversible self-assembly of patchy particles into monodisperse icosahedral clusters. J. Chem. Phys., 127(8):085106, 2007
A. W. Wilber, J. P. K. Doye, and A. A. Louis. Self-assembly of monodisperse clusters: dependence on target geometry. J. Chem. Phys., 131:175101, 2009.
I. G. Johnston, A. A. Louis, and J. P. K. Doye. Modelling the self-assembly of virus capsids. J. Phys.: Condens. Matter, 22(10):104101, 2010.
M. Sales-Pardo et al. Mesoscopic modelling fo nucleic acid chain dynamics. Phys. Rev. E, 71:051902, 2005.
S. Whitelam and P. L. Geissler. Avoiding unphysical kinetic traps in Monte Carlo simulations of strongly attractive particles. J. Chem. Phys., 127:154101, 2007.
T. E. Ouldridge et al. The self-assembly of DNA Holliday junctions studied with a minimal model. J. Chem. Phys., 130:065101, 2009.
S. Whitelam et al. The role of collective motion in examples of coarsening and self-assembly. Soft Matter, 5(6):1521–1262, 2009.
E. Luijten. Fluid simulation with the geometric cluster monte carlo algorithm. Computing in Science & Engineering, 8(2):20–29, 2006.
A. Bhattacharyay and A. Troisi. Self-assembly of sparsely distributed molecules: An efficient cluster algorithm. Chem. Phys. Lett., 458(1–3):210–213, 2008.
N. G. Van Kampen. Stochastic processes in physics and chemistry. Elsevier, Amsterdam, 2007.
R. L. Davidchack, R. Handel, and M. V. Tretyakov. Langevin thermostat for rigid body dynamics. J. Chem. Phys., 130(23):234101, 2009.
P. Depa, C. Chen, and J. K. Maranas. Why are coarse-grained force fields too fast? a look at dynamics of four coarse-grained polymers. J. Chem. Phys., 134(1):014903, 2011.
M. Doi and S. F. Edwards. The theory of polymer dynamics. Oxford University Press, Oxford, 1986.
G. M. Torrie and J. P. Valleau. Nonphysical sampling distributions in Monte Carlo free-energy estimation: Umbrella sampling. J. Comp. Phys., 23:187–199, 1977.
S. Kumar et al. The weighted histogram analysis method for free-energy calculations on biomolecules. i. the method. J. Comput. Chem., 13(8):1011–1021, 1992.
R. J. Allen, P. B. Warren, and P. R. ten Wolde. Sampling rare switching events in biochemical networks. Phys. Rev. Lett., 94(1):018104, 2005.
R. J. Allen, C. Valeriani, and P. R. ten Wolde. Forward flux sampling for rare event simulations. J. Phys.: Condens. Matter, 21(46):463102, 2009.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Ouldridge, T.E. (2012). Methods. In: Coarse-Grained Modelling of DNA and DNA Self-Assembly. Springer Theses. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-30517-7_3
Download citation
DOI: https://doi.org/10.1007/978-3-642-30517-7_3
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-30516-0
Online ISBN: 978-3-642-30517-7
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)