383 research outputs found
Force-induced misfolding in RNA
RNA folding is a kinetic process governed by the competition of a large
number of structures stabilized by the transient formation of base pairs that
may induce complex folding pathways and the formation of misfolded structures.
Despite of its importance in modern biophysics, the current understanding of
RNA folding kinetics is limited by the complex interplay between the weak
base-pair interactions that stabilize the native structure and the disordering
effect of thermal forces. The possibility of mechanically pulling individual
molecules offers a new perspective to understand the folding of nucleic acids.
Here we investigate the folding and misfolding mechanism in RNA secondary
structures pulled by mechanical forces. We introduce a model based on the
identification of the minimal set of structures that reproduce the patterns of
force-extension curves obtained in single molecule experiments. The model
requires only two fitting parameters: the attempt frequency at the level of
individual base pairs and a parameter associated to a free energy correction
that accounts for the configurational entropy of an exponentially large number
of neglected secondary structures. We apply the model to interpret results
recently obtained in pulling experiments in the three-helix junction S15 RNA
molecule (RNAS15). We show that RNAS15 undergoes force-induced misfolding where
force favors the formation of a stable non-native hairpin. The model reproduces
the pattern of unfolding and refolding force-extension curves, the distribution
of breakage forces and the misfolding probability obtained in the experiments.Comment: 28 pages, 11 figure
Zero Temperature Properties of RNA Secondary Structures
We analyze different microscopic RNA models at zero temperature. We discuss
both the most simple model, that suffers a large degeneracy of the ground
state, and models in which the degeneracy has been remove, in a more or less
severe manner. We calculate low-energy density of states using a coupling
perturbing method, where the ground state of a modified Hamiltonian, that
repels the original ground state, is determined. We evaluate scaling exponents
starting from measurements of overlaps and energy differences. In the case of
models without accidental degeneracy of the ground state we are able to clearly
establish the existence of a glassy phase with .Comment: 20 pages including 9 eps figure
Statistical mechanics of secondary structures formed by random RNA sequences
The formation of secondary structures by a random RNA sequence is studied as
a model system for the sequence-structure problem omnipresent in biopolymers.
Several toy energy models are introduced to allow detailed analytical and
numerical studies. First, a two-replica calculation is performed. By mapping
the two-replica problem to the denaturation of a single homogeneous RNA in
6-dimensional embedding space, we show that sequence disorder is perturbatively
irrelevant, i.e., an RNA molecule with weak sequence disorder is in a molten
phase where many secondary structures with comparable total energy coexist. A
numerical study of various models at high temperature reproduces behaviors
characteristic of the molten phase. On the other hand, a scaling argument based
on the extremal statistics of rare regions can be constructed to show that the
low temperature phase is unstable to sequence disorder. We performed a detailed
numerical study of the low temperature phase using the droplet theory as a
guide, and characterized the statistics of large-scale, low-energy excitations
of the secondary structures from the ground state structure. We find the
excitation energy to grow very slowly (i.e., logarithmically) with the length
scale of the excitation, suggesting the existence of a marginal glass phase.
The transition between the low temperature glass phase and the high temperature
molten phase is also characterized numerically. It is revealed by a change in
the coefficient of the logarithmic excitation energy, from being disorder
dominated to entropy dominated.Comment: 24 pages, 16 figure
Capturing the essence of folding and functions of biomolecules using Coarse-Grained Models
The distances over which biological molecules and their complexes can
function range from a few nanometres, in the case of folded structures, to
millimetres, for example during chromosome organization. Describing phenomena
that cover such diverse length, and also time scales, requires models that
capture the underlying physics for the particular length scale of interest.
Theoretical ideas, in particular, concepts from polymer physics, have guided
the development of coarse-grained models to study folding of DNA, RNA, and
proteins. More recently, such models and their variants have been applied to
the functions of biological nanomachines. Simulations using coarse-grained
models are now poised to address a wide range of problems in biology.Comment: 37 pages, 8 figure
Single Molecule Statistics and the Polynucleotide Unzipping Transition
We present an extensive theoretical investigation of the mechanical unzipping
of double-stranded DNA under the influence of an applied force. In the limit of
long polymers, there is a thermodynamic unzipping transition at a critical
force value of order 10 pN, with different critical behavior for homopolymers
and for random heteropolymers. We extend results on the disorder-averaged
behavior of DNA's with random sequences to the more experimentally accessible
problem of unzipping a single DNA molecule. As the applied force approaches the
critical value, the double-stranded DNA unravels in a series of discrete,
sequence-dependent steps that allow it to reach successively deeper energy
minima. Plots of extension versus force thus take the striking form of a series
of plateaus separated by sharp jumps. Similar qualitative features should
reappear in micromanipulation experiments on proteins and on folded RNA
molecules. Despite their unusual form, the extension versus force curves for
single molecules still reveal remnants of the disorder-averaged critical
behavior. Above the transition, the dynamics of the unzipping fork is related
to that of a particle diffusing in a random force field; anomalous,
disorder-dominated behavior is expected until the applied force exceeds the
critical value for unzipping by roughly 5 pN.Comment: 40 pages, 18 figure
Verification of the Crooks fluctuation theorem and recovery of RNA folding free energies
The description of nonequilibrium processes in nano-sized objects, where the
typical energies involved are a few times, is increasingly becoming central to
disciplines as diverse as condensed-matter physics, materials science, and
biophysics. Major recent developments towards a unified treatment of
arbitrarily large fluctuations in small systems are described by fluctuation
theorems that relate the probabilities of a system absorbing from or releasing
to the bath a given amount of energy in a nonequilibrium process. Here we
experimentally verify the Crooks Fluctuation Theorem (CFT) under weak and
strong nonequilibrium conditions by using optical tweezers to measure the
irreversible mechanical work during the unfolding and refolding of a small RNA
hairpin and an RNA three-helix junction. We also show that the CFT provides a
powerful way to obtain folding free energies in biomolecules by determining the
crossing between the unfolding and refolding irreversible work distributions.
The method makes it possible to obtain folding free energies in nonequilibrium
processes that dissipate up to of the average total work exerted, thereby
paving the way for reconstructing free energy landscapes along reaction
coordinates in nonequilibrium single-molecule experiments.Comment: PDF file, 19 pages. Supplementary information available online at
www.nature.co
ViennaRNA Package 2.0
<p>Abstract</p> <p>Background</p> <p>Secondary structure forms an important intermediate level of description of nucleic acids that encapsulates the dominating part of the folding energy, is often well conserved in evolution, and is routinely used as a basis to explain experimental findings. Based on carefully measured thermodynamic parameters, exact dynamic programming algorithms can be used to compute ground states, base pairing probabilities, as well as thermodynamic properties.</p> <p>Results</p> <p>The <monospace>ViennaRNA</monospace> Package has been a widely used compilation of RNA secondary structure related computer programs for nearly two decades. Major changes in the structure of the standard energy model, the <it>Turner 2004 </it>parameters, the pervasive use of multi-core CPUs, and an increasing number of algorithmic variants prompted a major technical overhaul of both the underlying <monospace>RNAlib</monospace> and the interactive user programs. New features include an expanded repertoire of tools to assess RNA-RNA interactions and restricted ensembles of structures, additional output information such as <it>centroid </it>structures and <it>maximum expected accuracy </it>structures derived from base pairing probabilities, or <it>z</it>-<it>scores </it>for locally stable secondary structures, and support for input in <monospace>fasta</monospace> format. Updates were implemented without compromising the computational efficiency of the core algorithms and ensuring compatibility with earlier versions.</p> <p>Conclusions</p> <p>The <monospace>ViennaRNA Package 2.0</monospace>, supporting concurrent computations <monospace>via OpenMP</monospace>, can be downloaded from <url>http://www.tbi.univie.ac.at/RNA</url>.</p
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