141
Chapter 5
Minimal Models for the Structure
and Dynamics of Nucleic Acids
Changbong Hyeon and Devarajan (Dave) Thirumalai
5.1 INTRODUCTION
e description of reality using models, the detail of which depends on the phe-
nomenon of interest, requires an appropriate level of abstraction, which depends
on the question of interest. For example, near a critical point, exponents that
describe the vanishing of order parameter or divergence of correlation length
are universal, depending only on the dimensionality (d), and are impervious to
atomic details. ese ndings, which are rooted in the concepts of universality
CONTENTS
5.1 Introduction 141
5.2 Polymer Models for dsDNA and Chromosome Structure 142
5.2.1 Looping Dynamics 142
5.2.2 Stretching dsDNA 144
5.2.3 Conned Polymers and Bacterial Chromosome Segregation 145
5.2.4 Chromosome Folding 146
5.3 RNA Folding 146
5.3.1 ree-Interaction-Site Model 147
5.3.2 Forced Unfolding of P5GA Using the TIS Model 150
5.3.3 Force-Quench Refolding 154
5.3.4 Complexity of Hairpin Formation 155
5.3.5 Self-Organized Polymer (SOP) Model for RNA Folding 156
5.3.6 Stretching Azoarcus Ribozyme 156
5.4 Concluding Remarks 159
Acknowledgments 160
References 160
Minimal Models for the Structure and Dynamics of Nucleic Acids
142
and renormalization group [1], are also applicable to the properties of poly-
mers [2]. For example, the size of a long homopolymer and the distribution of
end-to-end distance depend only on the solvent quality, the degree of polym-
erization, and d, but not on the details of monomer structure [2]. However, to
describe the dynamics occurring on length scales that are on the order of a few
nm, one has to contend with chemical properties of the monomer.
Without rigorous theoretical underpinnings, intuitive arguments and phe-
nomenology are often used in modeling complex biological processes. Here,
also the level of description depends on length scales. In nucleic acids, at short
length scales (l < 5 Å), detailed chemical environment determines the basic
forces (hydrogen bonds and dispersion forces) between two nucleotides. On the
scale l 1−3 nm interactions between two bases, base stacks and grooves of
the nucleic acids become relevant. Understanding how RNA folds (l 1−3 nm)
requires energy functions that provide at least a CG description of nucleotides
and interactions between them in the native state and excitations around the
folded structure. On the persistence-length scale l
p
150 bp 50 nm [3] and
beyond, it suces to treat double-stranded DNA (dsDNA) as a sti elastic la-
ment without explicitly capturing the base pairs. If l O(1) μm, dsDNA behaves
like a self-avoiding polymer [4]. On the scale of chromosomes (l mm), a much
coarser description suces. us, models for nucleic acids vary because the
scale of structural organization changes from nearly mm in chromosome to
several nm in the folded states of RNA.
5.2 POLYMER MODELS FOR dsDNA
ANDCHROMOSOME STRUCTURE
e length, L, of dsDNA exceeds a few μm with persistence length, l
p
50 nm.
On these scales, global properties of dsDNA, such as the end-to-end distance
and the dependence of l
p
on salt concentration, are not greatly aected by uc-
tuations of individual base pairs. Consequently, dsDNA can be treated as a
uctuating elastic material, for which the wormlike chain (WLC) is a suitable
polymer model. On much longer scales (L 1 mm, L/l
p
1), which is relevant
to chromosome, the genomic material can be described as a exible polymer.
Using these scale-dependent models, a number of predictions for DNA organi-
zation and dynamics can be made.
5.2.1 Looping Dynamics
Loop formation in biopolymers is an elementary process in the self-assembly
of DNA, RNA, and proteins. However, understanding cyclization kinetics is
complicated because multiple-length scales and internal chain modes are

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