728 research outputs found
Prediction of RNA pseudoknots by Monte Carlo simulations
In this paper we consider the problem of RNA folding with pseudoknots. We use
a graphical representation in which the secondary structures are described by
planar diagrams. Pseudoknots are identified as non-planar diagrams. We analyze
the non-planar topologies of RNA structures and propose a classification of RNA
pseudoknots according to the minimal genus of the surface on which the RNA
structure can be embedded. This classification provides a simple and natural
way to tackle the problem of RNA folding prediction in presence of pseudoknots.
Based on that approach, we describe a Monte Carlo algorithm for the prediction
of pseudoknots in an RNA molecule.Comment: 22 pages, 14 figure
Improved RNA pseudoknots prediction and classification using a new topological invariant
We propose a new topological characterization of RNA secondary structures
with pseudoknots based on two topological invariants. Starting from the classic
arc-representation of RNA secondary structures, we consider a model that
couples both I) the topological genus of the graph and II) the number of
crossing arcs of the corresponding primitive graph. We add a term proportional
to these topological invariants to the standard free energy of the RNA
molecule, thus obtaining a novel free energy parametrization which takes into
account the abundance of topologies of RNA pseudoknots observed in RNA
databases.Comment: 9 pages, 6 figure
A steepest descent calculation of RNA pseudoknots
We enumerate possible topologies of pseudoknots in single-stranded RNA
molecules. We use a steepest-descent approximation in the large N matrix field
theory, and a Feynman diagram formalism to describe the resulting pseudoknot
structure
Fluctuations in the Ensemble of Reaction Pathways
The dominant reaction pathway (DRP) is a rigorous framework to
microscopically compute the most probable trajectories, in non-equilibrium
transitions. In the low-temperature regime, such dominant pathways encode the
information about the reaction mechanism and can be used to estimate
non-equilibrium averages of arbitrary observables. On the other hand, at
sufficiently high temperatures, the stochastic fluctuations around the dominant
paths become important and have to be taken into account. In this work, we
develop a technique to systematically include the effects of such stochastic
fluctuations, to order k_B T. This method is used to compute the probability
for a transition to take place through a specific reaction channel and to
evaluate the reaction rate
The Metric of Yang-Mills Orbit Space on the Lattice
We find coordinates, the metric tensor, the inverse metric tensor and the
Laplace-Beltrami operator for the orbit space of Hamiltonian SU(2) gauge theory
on a finite, rectangular lattice. This is done using a complete axial gauge
fixing. The Gribov problem can be completely solved, with no remaining gauge
ambiguities.Comment: Title is changed in journal. Now 19 pages, still one figure, AMSTe
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