836 research outputs found
Asynchronous simulation of Boolean networks by monotone Boolean networks
International audienceWe prove that the fully asynchronous dynamics of a Boolean network f : {0, 1}^n → {0, 1}^n without negative loop can be simulated, in a very specific way, by a monotone Boolean network with 2n components. We then use this result to prove that, for every even n, there exists a monotone Boolean network f : {0, 1}^n → {0, 1}^n , an initial configuration x and a fixed point y of f such that: (i) y can be reached from x with a fully asynchronous updating strategy, and (ii) all such strategies contains at least 2^{n/2} updates. This contrasts with the following known property: if f : {0, 1}^n → {0, 1}^n is monotone, then, for every initial configuration x, there exists a fixed point y such that y can be reached from x with a fully asynchronous strategy that contains at most n updates
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
Partial Order on the set of Boolean Regulatory Functions
Logical models have been successfully used to describe regulatory and
signaling networks without requiring quantitative data. However, existing data
is insufficient to adequately define a unique model, rendering the
parametrization of a given model a difficult task.
Here, we focus on the characterization of the set of Boolean functions
compatible with a given regulatory structure, i.e. the set of all monotone
nondegenerate Boolean functions. We then propose an original set of rules to
locally explore the direct neighboring functions of any function in this set,
without explicitly generating the whole set. Also, we provide relationships
between the regulatory functions and their corresponding dynamics.
Finally, we illustrate the usefulness of this approach by revisiting
Probabilistic Boolean Networks with the model of T helper cell differentiation
from Mendoza & Xenarios
Dichotomy Results for Fixed-Point Existence Problems for Boolean Dynamical Systems
A complete classification of the computational complexity of the fixed-point
existence problem for boolean dynamical systems, i.e., finite discrete
dynamical systems over the domain {0, 1}, is presented. For function classes F
and graph classes G, an (F, G)-system is a boolean dynamical system such that
all local transition functions lie in F and the underlying graph lies in G. Let
F be a class of boolean functions which is closed under composition and let G
be a class of graphs which is closed under taking minors. The following
dichotomy theorems are shown: (1) If F contains the self-dual functions and G
contains the planar graphs then the fixed-point existence problem for (F,
G)-systems with local transition function given by truth-tables is NP-complete;
otherwise, it is decidable in polynomial time. (2) If F contains the self-dual
functions and G contains the graphs having vertex covers of size one then the
fixed-point existence problem for (F, G)-systems with local transition function
given by formulas or circuits is NP-complete; otherwise, it is decidable in
polynomial time.Comment: 17 pages; this version corrects an error/typo in the 2008/01/24
versio
Complementing ODE-Based System Analysis Using Boolean Networks Derived from an Euler-Like Transformation
In this paper, we present a systematic transition scheme for a large class of
ordinary differential equations (ODEs) into Boolean networks. Our transition
scheme can be applied to any system of ODEs whose right hand sides can be
written as sums and products of monotone functions. It performs an Euler-like
step which uses the signs of the right hand sides to obtain the Boolean update
functions for every variable of the corresponding discrete model. The discrete
model can, on one hand, be considered as another representation of the
biological system or, alternatively, it can be used to further the analysis of
the original ODE model. Since the generic transformation method does not
guarantee any property conservation, a subsequent validation step is required.
Depending on the purpose of the model this step can be based on experimental
data or ODE simulations and characteristics. Analysis of the resulting Boolean
model, both on its own and in comparison with the ODE model, then allows to
investigate system properties not accessible in a purely continuous setting.
The method is exemplarily applied to a previously published model of the
bovine estrous cycle, which leads to new insights regarding the regulation
among the components, and also indicates strongly that the system is tailored
to generate stable oscillations
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