271 research outputs found
ADAM: Analysis of Discrete Models of Biological Systems Using Computer Algebra
Background: Many biological systems are modeled qualitatively with discrete
models, such as probabilistic Boolean networks, logical models, Petri nets, and
agent-based models, with the goal to gain a better understanding of the system.
The computational complexity to analyze the complete dynamics of these models
grows exponentially in the number of variables, which impedes working with
complex models. Although there exist sophisticated algorithms to determine the
dynamics of discrete models, their implementations usually require
labor-intensive formatting of the model formulation, and they are oftentimes
not accessible to users without programming skills. Efficient analysis methods
are needed that are accessible to modelers and easy to use. Method: By
converting discrete models into algebraic models, tools from computational
algebra can be used to analyze their dynamics. Specifically, we propose a
method to identify attractors of a discrete model that is equivalent to solving
a system of polynomial equations, a long-studied problem in computer algebra.
Results: A method for efficiently identifying attractors, and the web-based
tool Analysis of Dynamic Algebraic Models (ADAM), which provides this and other
analysis methods for discrete models. ADAM converts several discrete model
types automatically into polynomial dynamical systems and analyzes their
dynamics using tools from computer algebra. Based on extensive experimentation
with both discrete models arising in systems biology and randomly generated
networks, we found that the algebraic algorithms presented in this manuscript
are fast for systems with the structure maintained by most biological systems,
namely sparseness, i.e., while the number of nodes in a biological network may
be quite large, each node is affected only by a small number of other nodes,
and robustness, i.e., small number of attractors
Therapeutic target discovery using Boolean network attractors: avoiding pathological phenotypes
Target identification, one of the steps of drug discovery, aims at
identifying biomolecules whose function should be therapeutically altered in
order to cure the considered pathology. This work proposes an algorithm for in
silico target identification using Boolean network attractors. It assumes that
attractors of dynamical systems, such as Boolean networks, correspond to
phenotypes produced by the modeled biological system. Under this assumption,
and given a Boolean network modeling a pathophysiology, the algorithm
identifies target combinations able to remove attractors associated with
pathological phenotypes. It is tested on a Boolean model of the mammalian cell
cycle bearing a constitutive inactivation of the retinoblastoma protein, as
seen in cancers, and its applications are illustrated on a Boolean model of
Fanconi anemia. The results show that the algorithm returns target combinations
able to remove attractors associated with pathological phenotypes and then
succeeds in performing the proposed in silico target identification. However,
as with any in silico evidence, there is a bridge to cross between theory and
practice, thus requiring it to be used in combination with wet lab experiments.
Nevertheless, it is expected that the algorithm is of interest for target
identification, notably by exploiting the inexpensiveness and predictive power
of computational approaches to optimize the efficiency of costly wet lab
experiments.Comment: Since the publication of this article and among the possible
improvements mentioned in the Conclusion, two improvements have been done:
extending the algorithm for multivalued logic and considering the basins of
attraction of the pathological attractors for selecting the therapeutic
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Using synchronous Boolean networks to model several phenomena of collective behavior
In this paper, we propose an approach for modeling and analysis of a number
of phenomena of collective behavior. By collectives we mean multi-agent systems
that transition from one state to another at discrete moments of time. The
behavior of a member of a collective (agent) is called conforming if the
opinion of this agent at current time moment conforms to the opinion of some
other agents at the previous time moment. We presume that at each moment of
time every agent makes a decision by choosing from the set {0,1} (where
1-decision corresponds to action and 0-decision corresponds to inaction). In
our approach we model collective behavior with synchronous Boolean networks. We
presume that in a network there can be agents that act at every moment of time.
Such agents are called instigators. Also there can be agents that never act.
Such agents are called loyalists. Agents that are neither instigators nor
loyalists are called simple agents. We study two combinatorial problems. The
first problem is to find a disposition of instigators that in several time
moments transforms a network from a state where a majority of simple agents are
inactive to a state with a majority of active agents. The second problem is to
find a disposition of loyalists that returns the network to a state with a
majority of inactive agents. Similar problems are studied for networks in which
simple agents demonstrate the contrary to conforming behavior that we call
anticonforming. We obtained several theoretical results regarding the behavior
of collectives of agents with conforming or anticonforming behavior. In
computational experiments we solved the described problems for randomly
generated networks with several hundred vertices. We reduced corresponding
combinatorial problems to the Boolean satisfiability problem (SAT) and used
modern SAT solvers to solve the instances obtained
Modeling multi-valued biological interaction networks using Fuzzy Answer Set Programming
Fuzzy Answer Set Programming (FASP) is an extension of the popular Answer Set Programming (ASP) paradigm that allows for modeling and solving combinatorial search problems in continuous domains. The recent development of practical solvers for FASP has enabled its applicability to real-world problems. In this paper, we investigate the application of FASP in modeling the dynamics of Gene Regulatory Networks (GRNs). A commonly used simplifying assumption to model the dynamics of GRNs is to assume only Boolean levels of activation of each node. Our work extends this Boolean network formalism by allowing multi-valued activation levels. We show how FASP can be used to model the dynamics of such networks. We experimentally assess the efficiency of our method using real biological networks found in the literature, as well as on randomly-generated synthetic networks. The experiments demonstrate the applicability and usefulness of our proposed method to find network attractors
Reducing Boolean Networks with Backward Boolean Equivalence
Boolean Networks (BNs) are established models to qualitatively describe
biological systems. The analysis of BNs might be infeasible for medium to large
BNs due to the state-space explosion problem. We propose a novel reduction
technique called \emph{Backward Boolean Equivalence} (BBE), which preserves
some properties of interest of BNs. In particular, reduced BNs provide a
compact representation by grouping variables that, if initialized equally, are
always updated equally. The resulting reduced state space is a subset of the
original one, restricted to identical initialization of grouped variables. The
corresponding trajectories of the original BN can be exactly restored. We show
the effectiveness of BBE by performing a large-scale validation on the whole
GINsim BN repository. In selected cases, we show how our method enables
analyses that would be otherwise intractable. Our method complements, and can
be combined with, other reduction methods found in the literature
Approximating attractors of Boolean networks by iterative CTL model checking
This paper introduces the notion of approximating asynchronous attractors of
Boolean networks by minimal trap spaces. We define three criteria for
determining the quality of an approximation: “faithfulness” which requires
that the oscillating variables of all attractors in a trap space correspond to
their dimensions, “univocality” which requires that there is a unique
attractor in each trap space, and “completeness” which requires that there are
no attractors outside of a given set of trap spaces. Each is a reachability
property for which we give equivalent model checking queries. Whereas
faithfulness and univocality can be decided by model checking the
corresponding subnetworks, the naive query for completeness must be evaluated
on the full state space. Our main result is an alternative approach which is
based on the iterative refinement of an initially poor approximation. The
algorithm detects so-called autonomous sets in the interaction graph,
variables that contain all their regulators, and considers their intersection
and extension in order to perform model checking on the smallest possible
state spaces. A benchmark, in which we apply the algorithm to 18 published
Boolean networks, is given. In each case, the minimal trap spaces are
faithful, univocal, and complete, which suggests that they are in general good
approximations for the asymptotics of Boolean networks
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