Delay-induced patterns in a two-dimensional lattice of coupled oscillators

We show how a variety of stable spatio-temporal periodic patterns can be created in 2D-lattices of coupled oscillators with non-homogeneous coupling delays. A "hybrid dispersion relation" is introduced, which allows studying the stability of time-periodic patterns analytically in the limit of large delay. The results are illustrated using the FitzHugh-Nagumo coupled neurons as well as coupled limit cycle (Stuart-Landau) oscillators

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

Control of stochastic and induced switching in biophysical networks

Noise caused by fluctuations at the molecular level is a fundamental part of intracellular processes. While the response of biological systems to noise has been studied extensively, there has been limited understanding of how to exploit it to induce a desired cell state. Here we present a scalable, quantitative method based on the Freidlin-Wentzell action to predict and control noise-induced switching between different states in genetic networks that, conveniently, can also control transitions between stable states in the absence of noise. We apply this methodology to models of cell differentiation and show how predicted manipulations of tunable factors can induce lineage changes, and further utilize it to identify new candidate strategies for cancer therapy in a cell death pathway model. This framework offers a systems approach to identifying the key factors for rationally manipulating biophysical dynamics, and should also find use in controlling other classes of noisy complex networks.Comment: A ready-to-use code package implementing the method described here is available from the authors upon reques

Scale-Free topologies and Activatory-Inhibitory interactions

A simple model of activatory-inhibitory interactions controlling the activity of agents (substrates) through a "saturated response" dynamical rule in a scale-free network is thoroughly studied. After discussing the most remarkable dynamical features of the model, namely fragmentation and multistability, we present a characterization of the temporal (periodic and chaotic) fluctuations of the quasi-stasis asymptotic states of network activity. The double (both structural and dynamical) source of entangled complexity of the system temporal fluctuations, as an important partial aspect of the Correlation Structure-Function problem, is further discussed to the light of the numerical results, with a view on potential applications of these general results.Comment: Revtex style, 12 pages and 12 figures. Enlarged manuscript with major revision and new results incorporated. To appear in Chaos (2006