3,586 research outputs found
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
A self-organized model for cell-differentiation based on variations of molecular decay rates
Systemic properties of living cells are the result of molecular dynamics
governed by so-called genetic regulatory networks (GRN). These networks capture
all possible features of cells and are responsible for the immense levels of
adaptation characteristic to living systems. At any point in time only small
subsets of these networks are active. Any active subset of the GRN leads to the
expression of particular sets of molecules (expression modes). The subsets of
active networks change over time, leading to the observed complex dynamics of
expression patterns. Understanding of this dynamics becomes increasingly
important in systems biology and medicine. While the importance of
transcription rates and catalytic interactions has been widely recognized in
modeling genetic regulatory systems, the understanding of the role of
degradation of biochemical agents (mRNA, protein) in regulatory dynamics
remains limited. Recent experimental data suggests that there exists a
functional relation between mRNA and protein decay rates and expression modes.
In this paper we propose a model for the dynamics of successions of sequences
of active subnetworks of the GRN. The model is able to reproduce key
characteristics of molecular dynamics, including homeostasis, multi-stability,
periodic dynamics, alternating activity, differentiability, and self-organized
critical dynamics. Moreover the model allows to naturally understand the
mechanism behind the relation between decay rates and expression modes. The
model explains recent experimental observations that decay-rates (or turnovers)
vary between differentiated tissue-classes at a general systemic level and
highlights the role of intracellular decay rate control mechanisms in cell
differentiation.Comment: 16 pages, 5 figure
A stochastic and dynamical view of pluripotency in mouse embryonic stem cells
Pluripotent embryonic stem cells are of paramount importance for biomedical
research thanks to their innate ability for self-renewal and differentiation
into all major cell lines. The fateful decision to exit or remain in the
pluripotent state is regulated by complex genetic regulatory network. Latest
advances in transcriptomics have made it possible to infer basic topologies of
pluripotency governing networks. The inferred network topologies, however, only
encode boolean information while remaining silent about the roles of dynamics
and molecular noise in gene expression. These features are widely considered
essential for functional decision making. Herein we developed a framework for
extending the boolean level networks into models accounting for individual
genetic switches and promoter architecture which allows mechanistic
interrogation of the roles of molecular noise, external signaling, and network
topology. We demonstrate the pluripotent state of the network to be a broad
attractor which is robust to variations of gene expression. Dynamics of exiting
the pluripotent state, on the other hand, is significantly influenced by the
molecular noise originating from genetic switching events which makes cells
more responsive to extracellular signals. Lastly we show that steady state
probability landscape can be significantly remodeled by global gene switching
rates alone which can be taken as a proxy for how global epigenetic
modifications exert control over stability of pluripotent states.Comment: 11 pages, 7 figure
Reliability of genetic networks is evolvable
Control of the living cell functions with remarkable reliability despite the
stochastic nature of the underlying molecular networks -- a property presumably
optimized by biological evolution. We here ask to what extent the property of a
stochastic dynamical network to produce reliable dynamics is an evolvable
trait. Using an evolutionary algorithm based on a deterministic selection
criterion for the reliability of dynamical attractors, we evolve dynamical
networks of noisy discrete threshold nodes. We find that, starting from any
random network, reliability of the attractor landscape can often be achieved
with only few small changes to the network structure. Further, the evolvability
of networks towards reliable dynamics while retaining their function is
investigated and a high success rate is found.Comment: 5 pages, 3 figure
Response of Boolean networks to perturbations
We evaluate the probability that a Boolean network returns to an attractor
after perturbing h nodes. We find that the return probability as function of h
can display a variety of different behaviours, which yields insights into the
state-space structure. In addition to performing computer simulations, we
derive analytical results for several types of Boolean networks, in particular
for Random Boolean Networks. We also apply our method to networks that have
been evolved for robustness to small perturbations, and to a biological
example
Relative Stability of Network States in Boolean Network Models of Gene Regulation in Development
Progress in cell type reprogramming has revived the interest in Waddington's
concept of the epigenetic landscape. Recently researchers developed the
quasi-potential theory to represent the Waddington's landscape. The
Quasi-potential U(x), derived from interactions in the gene regulatory network
(GRN) of a cell, quantifies the relative stability of network states, which
determine the effort required for state transitions in a multi-stable dynamical
system. However, quasi-potential landscapes, originally developed for
continuous systems, are not suitable for discrete-valued networks which are
important tools to study complex systems. In this paper, we provide a framework
to quantify the landscape for discrete Boolean networks (BNs). We apply our
framework to study pancreas cell differentiation where an ensemble of BN models
is considered based on the structure of a minimal GRN for pancreas development.
We impose biologically motivated structural constraints (corresponding to
specific type of Boolean functions) and dynamical constraints (corresponding to
stable attractor states) to limit the space of BN models for pancreas
development. In addition, we enforce a novel functional constraint
corresponding to the relative ordering of attractor states in BN models to
restrict the space of BN models to the biological relevant class. We find that
BNs with canalyzing/sign-compatible Boolean functions best capture the dynamics
of pancreas cell differentiation. This framework can also determine the genes'
influence on cell state transitions, and thus can facilitate the rational
design of cell reprogramming protocols.Comment: 24 pages, 6 figures, 1 tabl
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