Dynamical complexity of discrete-time regulatory networks
@article{Lima2005DynamicalCO, title={Dynamical complexity of discrete-time regulatory networks}, author={Ricardo Lima and Edgardo Ugalde}, journal={Nonlinearity}, year={2005}, volume={19}, pages={237 - 259} }
Genetic regulatory networks are usually modelled by systems of coupled differential equations, and more particularly by systems of piecewise affine differential equations. Finite state models, better known as logical networks, are also used. In this paper we present a class of models of regulatory networks which may be situated in the middle of the spectrum; they present both discrete and continuous aspects. They consist of a network of units, whose states are quantified by a continuous real…
31 Citations
Discrete time piecewise affine models of genetic regulatory networks
- 2006
Mathematics
Journal of mathematical biology
Simple models of genetic regulatory networks generated by piecewise affine contracting mappings whose variables represent gene expression levels are introduced and the mathematical analysis of their dynamics is presented.
Modular Gene Dynamics and Network Theory at Mesoscopic Scale
- 2009
Physics
This Thesis studies two-dimensional chaotic maps coupled through non-directed networks with different topologies and examines the dynamical relationship between these two network structures, examining the emergence of cooperativity on a large scale (trees) as a consequence of mesoscale dynamical patterns exhibited by the 4-star.
Open Regulatory Networks and Modularity
- 2009
Computer Science
We study the dynamical properties of small regulatory networks treated as non autonomous dynamical systems called modules when working inside larger networks or, equivalently when subject to external…
Robust stability analysis for discrete-time genetic regulatory networks with probabilistic time delays
- 2014
Mathematics
Neurocomputing
Stability and chaos in coupled two-dimensional maps on gene regulatory network of bacterium E. coli.
- 2010
Physics
Chaos
This work investigates the collective motion of Chirikov standard maps interacting with time delay through directed links of gene regulatory network of bacterium Escherichia coli and exhibits statistically robust self-organized dynamics in a weakly chaotic regime.
Beyond Periodicity for Piecewise Contracting Maps
- 2011
Mathematics
We study a wide class of dynamical systems defined by the iteration of piecewise contracting maps on compact and locally connected metric spaces. We consider non–isolated discontinuities and finitely…
Robust state estimation for discrete-time genetic regulatory network with random delays
- 2013
Mathematics, Engineering
Neurocomputing
Regulatory dynamics on random networks: asymptotic periodicity and modularity
- 2008
Mathematics, Computer Science
It is shown that, in a random regulatory network, initial conditions almost certainly converge to a periodic attractor, and it is proved that those modules are dynamically equivalent to independent regulatory networks.
29 References
Discrete time piecewise affine models of genetic regulatory networks
- 2006
Mathematics
Journal of mathematical biology
Simple models of genetic regulatory networks generated by piecewise affine contracting mappings whose variables represent gene expression levels are introduced and the mathematical analysis of their dynamics is presented.
Multistationarity, the basis of cell differentiation and memory. II. Logical analysis of regulatory networks in terms of feedback circuits.
- 2001
Mathematics
Chaos
This generalized logical description provides an image whose qualitative fit with the differential description is quite remarkable, and which tells which constraints on the logical parameters must be fulfilled in order for any circuit (or combination of circuits) to be functional.
Modeling and Simulation of Genetic Regulatory Systems: A Literature Review
- 2002
Biology
J. Comput. Biol.
This paper reviews formalisms that have been employed in mathematical biology and bioinformatics to describe genetic regulatory systems, in particular directed graphs, Bayesian networks, Boolean networks and their generalizations, ordinary and partial differential equations, qualitative differential equation, stochastic equations, and so on.
Combinatorial and topological methods in nonlinear chemical kinetics
- 1975
Mathematics
Combinatorial and topological techniques are developed to classify nonlinear chemical reaction networks in terms of their qualitative dynamics. A class of N coupled equations, based on a hypothesis…
A synthetic oscillatory network of transcriptional regulators
- 2000
Biology
Nature
This work used three transcriptional repressor systems that are not part of any natural biological clock to build an oscillating network, termed the repressilator, in Escherichia coli, which periodically induces the synthesis of green fluorescent protein as a readout of its state in individual cells.
Engineering stability in gene networks by autoregulation
- 2000
Biology
Nature
Simple gene circuits consisting of a regulator and transcriptional repressor modules in Escherichia coli are designed and constructed and the gain of stability produced by negative feedback is shown.
Dynamical behaviour of biological regulatory networks--II. Immunity control in bacteriophage lambda.
- 1995
Biology
Bulletin of mathematical biology
Boolean formalization of genetic control circuits.
- 1973
Computer Science
Journal of theoretical biology
Dynamics and Coding of a Biologically-Motivated Network
- 2006
Computer Science
Int. J. Bifurc. Chaos
A four-node network consisting of a negative circuit controlling a positive one is studied and conclusions drawn concerning the effectiveness of the p53 network as a tumor inhibitor mechanism are drawn.