542,410 research outputs found
Boolean versus continuous dynamics on simple two-gene modules
We investigate the dynamical behavior of simple modules composed of two genes
with two or three regulating connections. Continuous dynamics for mRNA and
protein concentrations is compared to a Boolean model for gene activity. Using
a generalized method, we study within a single framework different continuous
models and different types of regulatory functions, and establish conditions
under which the system can display stable oscillations. These conditions
concern the time scales, the degree of cooperativity of the regulating
interactions, and the signs of the interactions. Not all models that show
oscillations under Boolean dynamics can have oscillations under continuous
dynamics, and vice versa.Comment: 8 pages, 10 figure
Integrate and Fire Neural Networks, Piecewise Contractive Maps and Limit Cycles
We study the global dynamics of integrate and fire neural networks composed
of an arbitrary number of identical neurons interacting by inhibition and
excitation. We prove that if the interactions are strong enough, then the
support of the stable asymptotic dynamics consists of limit cycles. We also
find sufficient conditions for the synchronization of networks containing
excitatory neurons. The proofs are based on the analysis of the equivalent
dynamics of a piecewise continuous Poincar\'e map associated to the system. We
show that for strong interactions the Poincar\'e map is piecewise contractive.
Using this contraction property, we prove that there exist a countable number
of limit cycles attracting all the orbits dropping into the stable subset of
the phase space. This result applies not only to the Poincar\'e map under
study, but also to a wide class of general n-dimensional piecewise contractive
maps.Comment: 46 pages. In this version we added many comments suggested by the
referees all along the paper, we changed the introduction and the section
containing the conclusions. The final version will appear in Journal of
Mathematical Biology of SPRINGER and will be available at
http://www.springerlink.com/content/0303-681
A survey of methods for deciding whether a reaction network is multistationary
Which reaction networks, when taken with mass-action kinetics, have the
capacity for multiple steady states? There is no complete answer to this
question, but over the last 40 years various criteria have been developed that
can answer this question in certain cases. This work surveys these
developments, with an emphasis on recent results that connect the capacity for
multistationarity of one network to that of another. In this latter setting, we
consider a network that is embedded in a larger network , which means
that is obtained from by removing some subsets of chemical species and
reactions. This embedding relation is a significant generalization of the
subnetwork relation. For arbitrary networks, it is not true that if is
embedded in , then the steady states of lift to . Nonetheless, this
does hold for certain classes of networks; one such class is that of fully open
networks. This motivates the search for embedding-minimal multistationary
networks: those networks which admit multiple steady states but no proper,
embedded networks admit multiple steady states. We present results about such
minimal networks, including several new constructions of infinite families of
these networks
Communication Efficiency in Self-stabilizing Silent Protocols
Self-stabilization is a general paradigm to provide forward recovery
capabilities to distributed systems and networks. Intuitively, a protocol is
self-stabilizing if it is able to recover without external intervention from
any catastrophic transient failure. In this paper, our focus is to lower the
communication complexity of self-stabilizing protocols \emph{below} the need of
checking every neighbor forever. In more details, the contribution of the paper
is threefold: (i) We provide new complexity measures for communication
efficiency of self-stabilizing protocols, especially in the stabilized phase or
when there are no faults, (ii) On the negative side, we show that for
non-trivial problems such as coloring, maximal matching, and maximal
independent set, it is impossible to get (deterministic or probabilistic)
self-stabilizing solutions where every participant communicates with less than
every neighbor in the stabilized phase, and (iii) On the positive side, we
present protocols for coloring, maximal matching, and maximal independent set
such that a fraction of the participants communicates with exactly one neighbor
in the stabilized phase
Cell fate reprogramming by control of intracellular network dynamics
Identifying control strategies for biological networks is paramount for
practical applications that involve reprogramming a cell's fate, such as
disease therapeutics and stem cell reprogramming. Here we develop a novel
network control framework that integrates the structural and functional
information available for intracellular networks to predict control targets.
Formulated in a logical dynamic scheme, our approach drives any initial state
to the target state with 100% effectiveness and needs to be applied only
transiently for the network to reach and stay in the desired state. We
illustrate our method's potential to find intervention targets for cancer
treatment and cell differentiation by applying it to a leukemia signaling
network and to the network controlling the differentiation of helper T cells.
We find that the predicted control targets are effective in a broad dynamic
framework. Moreover, several of the predicted interventions are supported by
experiments.Comment: 61 pages (main text, 15 pages; supporting information, 46 pages) and
12 figures (main text, 6 figures; supporting information, 6 figures). In
revie
Random Boolean Network Models and the Yeast Transcriptional Network
The recently measured yeast transcriptional network is analyzed in terms of
simplified Boolean network models, with the aim of determining feasible rule
structures, given the requirement of stable solutions of the generated Boolean
networks. We find that for ensembles of generated models, those with canalyzing
Boolean rules are remarkably stable, whereas those with random Boolean rules
are only marginally stable. Furthermore, substantial parts of the generated
networks are frozen, in the sense that they reach the same state regardless of
initial state. Thus, our ensemble approach suggests that the yeast network
shows highly ordered dynamics.Comment: 23 pages, 5 figure
Evolution of Canalizing Boolean Networks
Boolean networks with canalizing functions are used to model gene regulatory
networks. In order to learn how such networks may behave under evolutionary
forces, we simulate the evolution of a single Boolean network by means of an
adaptive walk, which allows us to explore the fitness landscape. Mutations
change the connections and the functions of the nodes. Our fitness criterion is
the robustness of the dynamical attractors against small perturbations. We find
that with this fitness criterion the global maximum is always reached and that
there is a huge neutral space of 100% fitness. Furthermore, in spite of having
such a high degree of robustness, the evolved networks still share many
features with "chaotic" networks.Comment: 8 pages, 10 figures; revised and extended versio
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