4,697 research outputs found
A Monte Carlo Approach to Measure the Robustness of Boolean Networks
Emergence of robustness in biological networks is a paramount feature of
evolving organisms, but a study of this property in vivo, for any level of
representation such as Genetic, Metabolic, or Neuronal Networks, is a very hard
challenge. In the case of Genetic Networks, mathematical models have been used
in this context to provide insights on their robustness, but even in relatively
simple formulations, such as Boolean Networks (BN), it might not be feasible to
compute some measures for large system sizes. We describe in this work a Monte
Carlo approach to calculate the size of the largest basin of attraction of a
BN, which is intrinsically associated with its robustness, that can be used
regardless the network size. We show the stability of our method through
finite-size analysis and validate it with a full search on small networks.Comment: on 1st International Workshop on Robustness and Stability of
Biological Systems and Computational Solutions (WRSBS
Boolean decision problems with competing interactions on scale-free networks: Critical thermodynamics
We study the critical behavior of Boolean variables on scale-free networks
with competing interactions (Ising spin glasses). Our analytical results for
the disorder-network-decay-exponent phase diagram are verified using Monte
Carlo simulations. When the probability of positive (ferromagnetic) and
negative (antiferromagnetic) interactions is the same, the system undergoes a
finite-temperature spin-glass transition if the exponent that describes the
decay of the interaction degree in the scale-free graph is strictly larger than
3. However, when the exponent is equal to or less than 3, a spin-glass phase is
stable for all temperatures. The robustness of both the ferromagnetic and
spin-glass phases suggests that Boolean decision problems on scale-free
networks are quite stable to local perturbations. Finally, we show that for a
given decay exponent spin glasses on scale-free networks seem to obey
universality. Furthermore, when the decay exponent of the interaction degree is
larger than 4 in the spin-glass sector, the universality class is the same as
for the mean-field Sherrington-Kirkpatrick Ising spin glass.Comment: 14 pages, lots of figures and 2 table
Control of asymmetric Hopfield networks and application to cancer attractors
The asymmetric Hopfield model is used to simulate signaling dynamics in
gene/transcription factor networks. The model allows for a direct mapping of a
gene expression pattern into attractor states. We analyze different control
strategies aiming at disrupting attractor patterns using selective local fields
representing therapeutic interventions. The control strategies are based on the
identification of signaling , which are single nodes or strongly
connected clusters of nodes that have a large impact on the signaling. We
provide a theorem with bounds on the minimum number of nodes that guarantee
controllability of bottlenecks consisting of strongly connected components. The
control strategies are applied to the identification of sets of proteins that,
when inhibited, selectively disrupt the signaling of cancer cells while
preserving the signaling of normal cells. We use an experimentally validated
non-specific network and a specific B cell interactome reconstructed from gene
expression data to model cancer signaling in lung and B cells, respectively.
This model could help in the rational design of novel robust therapeutic
interventions based on our increasing knowledge of complex gene signaling
networks
Data-driven modelling of biological multi-scale processes
Biological processes involve a variety of spatial and temporal scales. A
holistic understanding of many biological processes therefore requires
multi-scale models which capture the relevant properties on all these scales.
In this manuscript we review mathematical modelling approaches used to describe
the individual spatial scales and how they are integrated into holistic models.
We discuss the relation between spatial and temporal scales and the implication
of that on multi-scale modelling. Based upon this overview over
state-of-the-art modelling approaches, we formulate key challenges in
mathematical and computational modelling of biological multi-scale and
multi-physics processes. In particular, we considered the availability of
analysis tools for multi-scale models and model-based multi-scale data
integration. We provide a compact review of methods for model-based data
integration and model-based hypothesis testing. Furthermore, novel approaches
and recent trends are discussed, including computation time reduction using
reduced order and surrogate models, which contribute to the solution of
inference problems. We conclude the manuscript by providing a few ideas for the
development of tailored multi-scale inference methods.Comment: This manuscript will appear in the Journal of Coupled Systems and
Multiscale Dynamics (American Scientific Publishers
The statistical mechanics of complex signaling networks : nerve growth factor signaling
It is becoming increasingly appreciated that the signal transduction systems
used by eukaryotic cells to achieve a variety of essential responses represent
highly complex networks rather than simple linear pathways. While significant
effort is being made to experimentally measure the rate constants for
individual steps in these signaling networks, many of the parameters required
to describe the behavior of these systems remain unknown, or at best,
estimates. With these goals and caveats in mind, we use methods of statistical
mechanics to extract useful predictions for complex cellular signaling
networks. To establish the usefulness of our approach, we have applied our
methods towards modeling the nerve growth factor (NGF)-induced differentiation
of neuronal cells. Using our approach, we are able to extract predictions that
are highly specific and accurate, thereby enabling us to predict the influence
of specific signaling modules in determining the integrated cellular response
to the two growth factors. We show that extracting biologically relevant
predictions from complex signaling models appears to be possible even in the
absence of measurements of all the individual rate constants. Our methods also
raise some interesting insights into the design and possible evolution of
cellular systems, highlighting an inherent property of these systems wherein
particular ''soft'' combinations of parameters can be varied over wide ranges
without impacting the final output and demonstrating that a few ''stiff''
parameter combinations center around the paramount regulatory steps of the
network. We refer to this property -- which is distinct from robustness -- as
''sloppiness.''Comment: 24 pages, 10 EPS figures, 1 GIF (makes 5 multi-panel figs + caption
for GIF), IOP style; supp. info/figs. included as brown_supp.pd
The Influence of Canalization on the Robustness of Boolean Networks
Time- and state-discrete dynamical systems are frequently used to model
molecular networks. This paper provides a collection of mathematical and
computational tools for the study of robustness in Boolean network models. The
focus is on networks governed by -canalizing functions, a recently
introduced class of Boolean functions that contains the well-studied class of
nested canalizing functions. The activities and sensitivity of a function
quantify the impact of input changes on the function output. This paper
generalizes the latter concept to -sensitivity and provides formulas for the
activities and -sensitivity of general -canalizing functions as well as
canalizing functions with more precisely defined structure. A popular measure
for the robustness of a network, the Derrida value, can be expressed as a
weighted sum of the -sensitivities of the governing canalizing functions,
and can also be calculated for a stochastic extension of Boolean networks.
These findings provide a computationally efficient way to obtain Derrida values
of Boolean networks, deterministic or stochastic, that does not involve
simulation.Comment: 16 pages, 2 figures, 3 table
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