11,782 research outputs found
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
Time-delayed models of gene regulatory networks
We discuss different mathematical models of gene regulatory networks as relevant to the onset and development of cancer. After discussion of alternativemodelling approaches, we use a paradigmatic two-gene network to focus on the role played by time delays in the dynamics of gene regulatory networks. We contrast the dynamics of the reduced model arising in the limit of fast mRNA dynamics with that of the full model. The review concludes with the discussion of some open problems
Stable and unstable attractors in Boolean networks
Boolean networks at the critical point have been a matter of debate for many
years as, e.g., scaling of number of attractor with system size. Recently it
was found that this number scales superpolynomially with system size, contrary
to a common earlier expectation of sublinear scaling. We here point to the fact
that these results are obtained using deterministic parallel update, where a
large fraction of attractors in fact are an artifact of the updating scheme.
This limits the significance of these results for biological systems where
noise is omnipresent. We here take a fresh look at attractors in Boolean
networks with the original motivation of simplified models for biological
systems in mind. We test stability of attractors w.r.t. infinitesimal
deviations from synchronous update and find that most attractors found under
parallel update are artifacts arising from the synchronous clocking mode. The
remaining fraction of attractors are stable against fluctuating response
delays. For this subset of stable attractors we observe sublinear scaling of
the number of attractors with system size.Comment: extended version, additional figur
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
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
Boolean Delay Equations: A simple way of looking at complex systems
Boolean Delay Equations (BDEs) are semi-discrete dynamical models with
Boolean-valued variables that evolve in continuous time. Systems of BDEs can be
classified into conservative or dissipative, in a manner that parallels the
classification of ordinary or partial differential equations. Solutions to
certain conservative BDEs exhibit growth of complexity in time. They represent
therewith metaphors for biological evolution or human history. Dissipative BDEs
are structurally stable and exhibit multiple equilibria and limit cycles, as
well as more complex, fractal solution sets, such as Devil's staircases and
``fractal sunbursts``. All known solutions of dissipative BDEs have stationary
variance. BDE systems of this type, both free and forced, have been used as
highly idealized models of climate change on interannual, interdecadal and
paleoclimatic time scales. BDEs are also being used as flexible, highly
efficient models of colliding cascades in earthquake modeling and prediction,
as well as in genetics. In this paper we review the theory of systems of BDEs
and illustrate their applications to climatic and solid earth problems. The
former have used small systems of BDEs, while the latter have used large
networks of BDEs. We moreover introduce BDEs with an infinite number of
variables distributed in space (``partial BDEs``) and discuss connections with
other types of dynamical systems, including cellular automata and Boolean
networks. This research-and-review paper concludes with a set of open
questions.Comment: Latex, 67 pages with 15 eps figures. Revised version, in particular
the discussion on partial BDEs is updated and enlarge
Topology of biological networks and reliability of information processing
Biological systems rely on robust internal information processing: Survival
depends on highly reproducible dynamics of regulatory processes. Biological
information processing elements, however, are intrinsically noisy (genetic
switches, neurons, etc.). Such noise poses severe stability problems to system
behavior as it tends to desynchronize system dynamics (e.g. via fluctuating
response or transmission time of the elements). Synchronicity in parallel
information processing is not readily sustained in the absence of a central
clock. Here we analyze the influence of topology on synchronicity in networks
of autonomous noisy elements. In numerical and analytical studies we find a
clear distinction between non-reliable and reliable dynamical attractors,
depending on the topology of the circuit. In the reliable cases, synchronicity
is sustained, while in the unreliable scenario, fluctuating responses of single
elements can gradually desynchronize the system, leading to non-reproducible
behavior. We find that the fraction of reliable dynamical attractors strongly
correlates with the underlying circuitry. Our model suggests that the observed
motif structure of biological signaling networks is shaped by the biological
requirement for reproducibility of attractors.Comment: 7 pages, 7 figure
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