514 research outputs found
The effect of negative feedback loops on the dynamics of Boolean networks
Feedback loops in a dynamic network play an important role in determining the
dynamics of that network. Through a computational study, in this paper we show
that networks with fewer independent negative feedback loops tend to exhibit
more regular behavior than those with more negative loops. To be precise, we
study the relationship between the number of independent feedback loops and the
number and length of the limit cycles in the phase space of dynamic Boolean
networks. We show that, as the number of independent negative feedback loops
increases, the number (length) of limit cycles tends to decrease (increase).
These conclusions are consistent with the fact, for certain natural biological
networks, that they on the one hand exhibit generally regular behavior and on
the other hand show less negative feedback loops than randomized networks with
the same numbers of nodes and connectivity
Monotone and near-monotone biochemical networks
Monotone subsystems have appealing properties as components of larger networks, since they exhibit robust dynamical stability and predictability of responses to perturbations. This suggests that natural biological systems may have evolved to be, if not monotone, at least close to monotone in the sense of being decomposable into a âsmallâ number of monotone components, In addition, recent research has shown that much insight can be attained from decomposing networks into monotone subsystems and the analysis of the resulting interconnections using tools from control theory. This paper provides an expository introduction to monotone systems and their interconnections, describing the basic concepts and some of the main mathematical results in a largely informal fashion
Symbolic numeric analysis of attractors in randomly generated piecewise affine models of gene networks
International audienceThe goal of this paper is to present and experiment the computer aided analysis of phase portraits of some ordinary differential equations. The latter are piecewise affine, and have been primitively introduced as coarse-grained models of gene regulatory networks. Their simple formulation allows for numerical investigation, but their typical phase portrait is still largely unknown. They have been shown to present all the main aspects of nonlinear dynamics, including chaos. But it is still of interest to simulate random versions of these models, and to count and classify their attractors. This paper presents algorithms that allow for an automatic treatment of this kind, and apply it to four-dimensional sample systems. Contrary to previous studies, the latter have several thresholds in each direction, a fact whose consequences on the number and nature of attractors is discussed
Limit cycles in piecewise-affine gene network models with multiple interaction loops
In this paper we consider piecewise affine differential equations modeling
gene networks. We work with arbitrary decay rates, and under a local hypothesis
expressed as an alignment condition of successive focal points. The interaction
graph of the system may be rather complex (multiple intricate loops of any
sign, multiple thresholds...). Our main result is an alternative theorem
showing that, if a sequence of region is periodically visited by trajectories,
then under our hypotheses, there exists either a unique stable periodic
solution, or the origin attracts all trajectories in this sequence of regions.
This result extends greatly our previous work on a single negative feedback
loop. We give several examples and simulations illustrating different cases
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
Periodic solutions of piecewise affine gene network models: the case of a negative feedback loop
In this paper the existence and unicity of a stable periodic orbit is proven,
for a class of piecewise affine differential equations in dimension 3 or more,
provided their interaction structure is a negative feedback loop. It is also
shown that the same systems converge toward a unique stable equilibrium point
in dimension 2. This extends a theorem of Snoussi, which showed the existence
of these orbits only. The considered class of equations is usually studied as a
model of gene regulatory networks. It is not assumed that all decay rates are
identical, which is biologically irrelevant, but has been done in the vast
majority of previous studies. Our work relies on classical results about fixed
points of monotone, concave operators acting on positive variables. Moreover,
the used techniques are very likely to apply in more general contexts, opening
directions for future work
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