15 research outputs found
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
Prediction of lethal and synthetically lethal knock-outs in regulatory networks
The complex interactions involved in regulation of a cell's function are
captured by its interaction graph. More often than not, detailed knowledge
about enhancing or suppressive regulatory influences and cooperative effects is
lacking and merely the presence or absence of directed interactions is known.
Here we investigate to which extent such reduced information allows to forecast
the effect of a knock-out or a combination of knock-outs. Specifically we ask
in how far the lethality of eliminating nodes may be predicted by their network
centrality, such as degree and betweenness, without knowing the function of the
system. The function is taken as the ability to reproduce a fixed point under a
discrete Boolean dynamics. We investigate two types of stochastically generated
networks: fully random networks and structures grown with a mechanism of node
duplication and subsequent divergence of interactions. On all networks we find
that the out-degree is a good predictor of the lethality of a single node
knock-out. For knock-outs of node pairs, the fraction of successors shared
between the two knocked-out nodes (out-overlap) is a good predictor of
synthetic lethality. Out-degree and out-overlap are locally defined and
computationally simple centrality measures that provide a predictive power
close to the optimal predictor.Comment: published version, 10 pages, 6 figures, 2 tables; supplement at
http://www.bioinf.uni-leipzig.de/publications/supplements/11-01
The effect of scale-free topology on the robustness and evolvability of genetic regulatory networks
We investigate how scale-free (SF) and Erdos-Renyi (ER) topologies affect the
interplay between evolvability and robustness of model gene regulatory networks
with Boolean threshold dynamics. In agreement with Oikonomou and Cluzel (2006)
we find that networks with SFin topologies, that is SF topology for incoming
nodes and ER topology for outgoing nodes, are significantly more evolvable
towards specific oscillatory targets than networks with ER topology for both
incoming and outgoing nodes. Similar results are found for networks with SFboth
and SFout topologies. The functionality of the SFout topology, which most
closely resembles the structure of biological gene networks (Babu et al.,
2004), is compared to the ER topology in further detail through an extension to
multiple target outputs, with either an oscillatory or a non-oscillatory
nature. For multiple oscillatory targets of the same length, the differences
between SFout and ER networks are enhanced, but for non-oscillatory targets
both types of networks show fairly similar evolvability. We find that SF
networks generate oscillations much more easily than ER networks do, and this
may explain why SF networks are more evolvable than ER networks are for
oscillatory phenotypes. In spite of their greater evolvability, we find that
networks with SFout topologies are also more robust to mutations than ER
networks. Furthermore, the SFout topologies are more robust to changes in
initial conditions (environmental robustness). For both topologies, we find
that once a population of networks has reached the target state, further
neutral evolution can lead to an increase in both the mutational robustness and
the environmental robustness to changes in initial conditions.Comment: 16 pages, 15 figure
Evolving Sensitivity Balances Boolean Networks
We investigate the sensitivity of Boolean Networks (BNs) to mutations. We are interested in Boolean Networks as a model of Gene Regulatory Networks (GRNs). We adopt Ribeiro and Kauffman’s Ergodic Set and use it to study the long term dynamics of a BN. We define the sensitivity of a BN to be the mean change in its Ergodic Set structure under all possible loss of interaction mutations. Insilico experiments were used to selectively evolve BNs for sensitivity to losing interactions. We find that maximum sensitivity was often achievable and resulted in the BNs becoming topologically balanced, i.e. they evolve towards network structures in which they have a similar number of inhibitory and excitatory interactions. In terms of the dynamics, the dominant sensitivity strategy that evolved was to build BNs with Ergodic Sets dominated by a single long limit cycle which is easily destabilised by mutations. We discuss the relevance of our findings in the context of Stem Cell Differentiation and propose a relationship between pluripotent stem cells and our evolved sensitive networks
Phase transitions and memory effects in the dynamics of Boolean networks
The generating functional method is employed to investigate the synchronous
dynamics of Boolean networks, providing an exact result for the system dynamics
via a set of macroscopic order parameters. The topology of the networks studied
and its constituent Boolean functions represent the system's quenched disorder
and are sampled from a given distribution. The framework accommodates a variety
of topologies and Boolean function distributions and can be used to study both
the noisy and noiseless regimes; it enables one to calculate correlation
functions at different times that are inaccessible via commonly used
approximations. It is also used to determine conditions for the annealed
approximation to be valid, explore phases of the system under different levels
of noise and obtain results for models with strong memory effects, where
existing approximations break down. Links between BN and general Boolean
formulas are identified and common results to both system types are
highlighted
Comparing the evolution of canalyzing and threshold networks
We study the influence of the type of update functions on the evolution of Boolean networks under selection for dynamical robustness. The chosen types of functions are canalyzing functions and threshold functions. Starting from a random initial network, we evolve the network by an adaptive walk. During the first time period, where the networks evolve to the plateau of 100Â percent fitness, we find that both type of update functions give the same behavior, albeit for different network sizes and connectedness. However, on the long run, as the networks continue to evolve on the fitness plateau, the different types of update functions give rise to different network structure, due to their different mutational robustness. When both types of update functions occur together, none of them is preferred under long-term evolution. Copyright EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2011
On the design of Boolean network robots
Dynamical systems theory and complexity science provide powerful tools for analysing artificial agents and robots. Furthermore, they have been recently proposed also as a source of design principles and guidelines. Boolean networks are a prominent example of complex dynamical systems and they have been shown to effectively capture important phenomena in gene regulation. From an engineering perspective, these models are very compelling, because they can exhibit rich and complex behaviours, in spite of the compactness of their description. In this paper, we propose the use of Boolean networks for controlling robots' behaviour. The network is designed by means of an automatic procedure based on stochastic local search techniques. We show that this approach makes it possible to design a network which enables the robot to accomplish a task that requires the capability of navigating the space using a light stimulus, as well as the formation and use of an internal memory. © 2011 Springer-Verlag.SCOPUS: cp.kinfo:eu-repo/semantics/publishe
The phase diagram of random Boolean networks with nested canalizing functions
We obtain the phase diagram of random Boolean networks with
nested canalizing functions. Using the annealed approximation, we
obtain the evolution of the number bt of nodes with value one, and
the network sensitivity λ, and compare with numerical
simulations of quenched networks. We find that, contrary to what was
reported by Kauffman et al. [Proc. Natl. Acad. Sci.
101, 17102 (2004)], these networks have a rich phase diagram, were
both the “chaotic" and frozen phases are present, as well as an
oscillatory regime of the value of bt. We argue that the presence
of only the frozen phase in the work of Kauffman et al. was
due simply to the specific parametrization used, and is not an
inherent feature of this class of functions. However, these networks
are significantly more stable than the variant where all possible
Boolean functions are allowed