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The dynamics of Boolean networks with scale-free topology are studied. The existence of a phase transition from ordered to chaotic dynamics, governed by the value of the scale-free exponent of the network, is shown analytically by analyzing the overlap between two distinct trajectories. The phase diagram shows that the phase transition occurs for values of… (More)

This paper reviews a class of generic dissipative dynamical systems called N-K models. In these models, the dynamics of N elements, defined as Boolean variables, develop step by step, clocked by a discrete time variable. Each of the N Boolean elements at a given time is given a value which depends upon K elements in the previous time step. We review the… (More)

- Maximino Aldana, Philippe Cluzel
- Proceedings of the National Academy of Sciences…
- 2003

As biological studies shift from molecular description to system analysis we need to identify the design principles of large intracellular networks. In particular, without knowing the molecular details, we want to determine how cells reliably perform essential intracellular tasks. Recent analyses of signaling pathways and regulatory transcription networks… (More)

- Maximino Aldana, Enrique Balleza, Stuart A. Kauffman, Osbaldo Resendiz
- Journal of theoretical biology
- 2007

Living organisms are robust to a great variety of genetic changes. Gene regulation networks and metabolic pathways self-organize and reaccommodate to make the organism perform with stability and reliability under many point mutations, gene duplications and gene deletions. At the same time, living organisms are evolvable, which means that these kind of… (More)

- Elena R. Alvarez-Buylla, Álvaro Chaos, +8 authors Pablo Padilla-Longoria
- PloS one
- 2008

In contrast to the classical view of development as a preprogrammed and deterministic process, recent studies have demonstrated that stochastic perturbations of highly non-linear systems may underlie the emergence and stability of biological patterns. Herein, we address the question of whether noise contributes to the generation of the stereotypical… (More)

- Ilya Shmulevich, Stuart A. Kauffman, Maximino Aldana
- Proceedings of the National Academy of Sciences…
- 2005

Two important theoretical approaches have been developed to generically characterize the relationship between the structure and function of large genetic networks: the continuous approach, based on reaction-kinetics differential equations, and the Boolean approach, based on difference equations and discrete logical rules. These two approaches do not always… (More)

The coordinated expression of the different genes in an organism is essential to sustain functionality under the random external perturbations to which the organism might be subjected. To cope with such external variability, the global dynamics of the genetic network must possess two central properties. (a) It must be robust enough as to guarantee stability… (More)

- Matti Nykter, Nathan D. Price, +5 authors Ilya Shmulevich
- Proceedings of the National Academy of Sciences…
- 2008

Cells are dynamical systems of biomolecular interactions that process information from their environment to mount diverse yet specific responses. A key property of many self-organized systems is that of criticality: a state of a system in which, on average, perturbations are neither dampened nor amplified, but are propagated over long temporal or spatial… (More)

We investigate the conditions that produce a phase transition from an ordered to a disordered state in a family of models of two-dimensional elements with a ferromagnetic-like interaction. This family is defined to contain under the same framework, among others, the XY-model and the Self-Driven Particles Model introduced by Vicsek et al. Each model is… (More)

- Christian Torres-Sosa, Sui Huang, Maximino Aldana
- PLoS Computational Biology
- 2012

Accumulating experimental evidence suggests that the gene regulatory networks of living organisms operate in the critical phase, namely, at the transition between ordered and chaotic dynamics. Such critical dynamics of the network permits the coexistence of robustness and flexibility which are necessary to ensure homeostatic stability (of a given phenotype)… (More)