49,812 research outputs found
Expected degree for RNA secondary structure networks
Consider the network of all secondary structures of a given RNA sequence,
where nodes are connected when the corresponding structures have base pair
distance one. The expected degree of the network is the average number of
neighbors, where average may be computed with respect to the either the uniform
or Boltzmann probability. Here we describe the first algorithm, RNAexpNumNbors,
that can compute the expected number of neighbors, or expected network degree,
of an input sequence. For RNA sequences from the Rfam database, the expected
degree is significantly less than the CMFE structure, defined to have minimum
free energy over all structures consistent with the Rfam consensus structure.
The expected degree of structural RNAs, such as purine riboswitches,
paradoxically appears to be smaller than that of random RNA, yet the difference
between the degree of the MFE structure and the expected degree is larger than
that of random RNA. Expected degree does not seem to correlate with standard
structural diversity measures of RNA, such as positional entropy, ensemble
defect, etc. The program {\tt RNAexpNumNbors} is written in C, runs in cubic
time and quadratic space, and is publicly available at
http://bioinformatics.bc.edu/clotelab/RNAexpNumNbors.Comment: 25 pages, 5 figures, 5 table
Effects of neutral selection on the evolution of molecular species
We introduce a new model of evolution on a fitness landscape possessing a
tunable degree of neutrality. The model allows us to study the general
properties of molecular species undergoing neutral evolution. We find that a
number of phenomena seen in RNA sequence-structure maps are present also in our
general model. Examples are the occurrence of "common" structures which occupy
a fraction of the genotype space which tends to unity as the length of the
genotype increases, and the formation of percolating neutral networks which
cover the genotype space in such a way that a member of such a network can be
found within a small radius of any point in the space. We also describe a
number of new phenomena which appear to be general properties of neutrally
evolving systems. In particular, we show that the maximum fitness attained
during the adaptive walk of a population evolving on such a fitness landscape
increases with increasing degree of neutrality, and is directly related to the
fitness of the most fit percolating network.Comment: 16 pages including 4 postscript figures, typeset in LaTeX2e using the
Elsevier macro package elsart.cl
Neutral networks of genotypes: Evolution behind the curtain
Our understanding of the evolutionary process has gone a long way since the
publication, 150 years ago, of "On the origin of species" by Charles R. Darwin.
The XXth Century witnessed great efforts to embrace replication, mutation, and
selection within the framework of a formal theory, able eventually to predict
the dynamics and fate of evolving populations. However, a large body of
empirical evidence collected over the last decades strongly suggests that some
of the assumptions of those classical models necessitate a deep revision. The
viability of organisms is not dependent on a unique and optimal genotype. The
discovery of huge sets of genotypes (or neutral networks) yielding the same
phenotype --in the last term the same organism--, reveals that, most likely,
very different functional solutions can be found, accessed and fixed in a
population through a low-cost exploration of the space of genomes. The
'evolution behind the curtain' may be the answer to some of the current puzzles
that evolutionary theory faces, like the fast speciation process that is
observed in the fossil record after very long stasis periods.Comment: 7 pages, 7 color figures, uses a modification of pnastwo.cls called
pnastwo-modified.cls (included
A tractable genotype-phenotype map for the self-assembly of protein quaternary structure
The mapping between biological genotypes and phenotypes is central to the
study of biological evolution. Here we introduce a rich, intuitive, and
biologically realistic genotype-phenotype (GP) map, that serves as a model of
self-assembling biological structures, such as protein complexes, and remains
computationally and analytically tractable. Our GP map arises naturally from
the self-assembly of polyomino structures on a 2D lattice and exhibits a number
of properties: (genotypes vastly outnumber phenotypes),
(genotypic redundancy varies greatly between
phenotypes), (phenotypes consist
of disconnected mutational networks) and (most
phenotypes can be reached in a small number of mutations). We also show that
the mutational robustness of phenotypes scales very roughly logarithmically
with phenotype redundancy and is positively correlated with phenotypic
evolvability. Although our GP map describes the assembly of disconnected
objects, it shares many properties with other popular GP maps for connected
units, such as models for RNA secondary structure or the HP lattice model for
protein tertiary structure. The remarkable fact that these important properties
similarly emerge from such different models suggests the possibility that
universal features underlie a much wider class of biologically realistic GP
maps.Comment: 12 pages, 6 figure
Encoding folding paths of RNA switches
RNA co-transcriptional folding has long been suspected to play an active role
in helping proper native folding of ribozymes and structured regulatory motifs
in mRNA untranslated regions. Yet, the underlying mechanisms and coding
requirements for efficient co-transcriptional folding remain unclear.
Traditional approaches have intrinsic limitations to dissect RNA folding paths,
as they rely on sequence mutations or circular permutations that typically
perturb both RNA folding paths and equilibrium structures. Here, we show that
exploiting sequence symmetries instead of mutations can circumvent this problem
by essentially decoupling folding paths from equilibrium structures of designed
RNA sequences. Using bistable RNA switches with symmetrical helices conserved
under sequence reversal, we demonstrate experimentally that native and
transiently formed helices can guide efficient co-transcriptional folding into
either long-lived structure of these RNA switches. Their folding path is
controlled by the order of helix nucleations and subsequent exchanges during
transcription, and may also be redirected by transient antisense interactions.
Hence, transient intra- and intermolecular base pair interactions can
effectively regulate the folding of nascent RNA molecules into different native
structures, provided limited coding requirements, as discussed from an
information theory perspective. This constitutive coupling between RNA
synthesis and RNA folding regulation may have enabled the early emergence of
autonomous RNA-based regulation networks.Comment: 9 pages, 6 figure
Statistical mechanics of RNA folding: importance of alphabet size
We construct a minimalist model of RNA secondary-structure formation and use
it to study the mapping from sequence to structure. There are strong,
qualitative differences between two-letter and four or six-letter alphabets.
With only two kinds of bases, there are many alternate folding configurations,
yielding thermodynamically stable ground-states only for a small set of
structures of high designability, i.e., total number of associated sequences.
In contrast, sequences made from four bases, as found in nature, or six bases
have far fewer competing folding configurations, resulting in a much greater
average stability of the ground state.Comment: 7 figures; uses revtex
A complex adaptive systems approach to the kinetic folding of RNA
The kinetic folding of RNA sequences into secondary structures is modeled as
a complex adaptive system, the components of which are possible RNA structural
rearrangements (SRs) and their associated bases and base pairs. RNA bases and
base pairs engage in local stacking interactions that determine the
probabilities (or fitnesses) of possible SRs. Meanwhile, selection operates at
the level of SRs; an autonomous stochastic process periodically (i.e., from one
time step to another) selects a subset of possible SRs for realization based on
the fitnesses of the SRs. Using examples based on selected natural and
synthetic RNAs, the model is shown to qualitatively reproduce characteristic
(nonlinear) RNA folding dynamics such as the attainment by RNAs of alternative
stable states. Possible applications of the model to the analysis of properties
of fitness landscapes, and of the RNA sequence to structure mapping are
discussed.Comment: 23 pages, 4 figures, 2 tables, to be published in BioSystems (Note:
updated 2 references
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