2,211 research outputs found
On the effects of firing memory in the dynamics of conjunctive networks
Boolean networks are one of the most studied discrete models in the context
of the study of gene expression. In order to define the dynamics associated to
a Boolean network, there are several \emph{update schemes} that range from
parallel or \emph{synchronous} to \emph{asynchronous.} However, studying each
possible dynamics defined by different update schemes might not be efficient.
In this context, considering some type of temporal delay in the dynamics of
Boolean networks emerges as an alternative approach. In this paper, we focus in
studying the effect of a particular type of delay called \emph{firing memory}
in the dynamics of Boolean networks. Particularly, we focus in symmetric
(non-directed) conjunctive networks and we show that there exist examples that
exhibit attractors of non-polynomial period. In addition, we study the
prediction problem consisting in determinate if some vertex will eventually
change its state, given an initial condition. We prove that this problem is
{\bf PSPACE}-complete
Emergence of robustness against noise: A structural phase transition in evolved models of gene regulatory networks
We investigate the evolution of Boolean networks subject to a selective
pressure which favors robustness against noise, as a model of evolved genetic
regulatory systems. By mapping the evolutionary process into a statistical
ensemble and minimizing its associated free energy, we find the structural
properties which emerge as the selective pressure is increased and identify a
phase transition from a random topology to a "segregated core" structure, where
a smaller and more densely connected subset of the nodes is responsible for
most of the regulation in the network. This segregated structure is very
similar qualitatively to what is found in gene regulatory networks, where only
a much smaller subset of genes --- those responsible for transcription factors
--- is responsible for global regulation. We obtain the full phase diagram of
the evolutionary process as a function of selective pressure and the average
number of inputs per node. We compare the theoretical predictions with Monte
Carlo simulations of evolved networks and with empirical data for Saccharomyces
cerevisiae and Escherichia coli.Comment: 12 pages, 10 figure
Quantification of reachable attractors in asynchronous discrete dynamics
Motivation: Models of discrete concurrent systems often lead to huge and
complex state transition graphs that represent their dynamics. This makes
difficult to analyse dynamical properties. In particular, for logical models of
biological regulatory networks, it is of real interest to study attractors and
their reachability from specific initial conditions, i.e. to assess the
potential asymptotical behaviours of the system. Beyond the identification of
the reachable attractors, we propose to quantify this reachability.
Results: Relying on the structure of the state transition graph, we estimate
the probability of each attractor reachable from a given initial condition or
from a portion of the state space. First, we present a quasi-exact solution
with an original algorithm called Firefront, based on the exhaustive
exploration of the reachable state space. Then, we introduce an adapted version
of Monte Carlo simulation algorithm, termed Avatar, better suited to larger
models. Firefront and Avatar methods are validated and compared to other
related approaches, using as test cases logical models of synthetic and
biological networks.
Availability: Both algorithms are implemented as Perl scripts that can be
freely downloaded from http://compbio.igc.gulbenkian.pt/nmd/node/59 along with
Supplementary Material.Comment: 19 pages, 2 figures, 2 algorithms and 2 table
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