The Role of Criticality of Gene Regulatory Networks in Morphogenesis

Hallmarks of criticality, such as power-laws and scale invariance, have been empirically found in cortical networks and it has been conjectured that operating at criticality entails functional advantages, such as optimal computational capabilities, memory, and large dynamical ranges. As critical behavior requires a high degree of fine tuning to emerge, some type of self-tuning mechanism needs to be invoked. Here we show that, taking into account the complex hierarchical-modul...

Interacting biological systems at all organizational levels display emergent behavior. Modeling these systems is made challenging by the number and variety of biological components and interactions (from molecules in gene regulatory networks to species in ecological networks) and the often-incomplete state of system knowledge (e.g., the unknown values of kinetic parameters for biochemical reactions). Boolean networks have emerged as a powerful tool for modeling these systems....

We present a model of adaptive regulatory networks consisting of a simple biologically-motivated rewiring procedure coupled to an elementary stability criterion. The resulting networks exhibit a characteristic stationary heavy-tailed degree distribution, show complex structural microdynamics and self-organize to a dynamically critical state. We show analytically that the observed criticality results from the formation and breaking of transient feedback loops during the adapti...

Criticality has been proposed as a mechanism for the emergence of complexity, life, and computation, as it exhibits a balance between robustness and adaptability. In classic models of complex systems where structure and dynamics are considered homogeneous, criticality is restricted to phase transitions, leading either to robust (ordered) or adaptive (chaotic) phases in most of the parameter space. Many real-world complex systems, however, are not homogeneous. Some elements ch...

It has been proposed that adaptation in complex systems is optimized at the critical boundary between ordered and disordered dynamical regimes. Here, we review models of evolving dynamical networks that lead to self-organization of network topology based on a local coupling between a dynamical order parameter and rewiring of network connectivity, with convergence towards criticality in the limit of large network size $N$. In particular, two adaptive schemes are discussed and ...

We apply complex network analysis to the state spaces of random Boolean networks (RBNs). An RBN contains $N$ Boolean elements each with $K$ inputs. A directed state space network (SSN) is constructed by linking each dynamical state, represented as a node, to its temporal successor. We study the heterogeneity of an SSN at both local and global scales, as well as sample-to-sample fluctuations within an ensemble of SSNs. We use in-degrees of nodes as a local topological measure,...

The preliminary analyses on a multiscale model of intestinal crypt dynamics are here presented. The model combines a morphological model, based on the Cellular Potts Model (CPM), and a gene regulatory network model, based on Noisy Random Boolean Networks (NRBNs). Simulations suggest that the stochastic differentiation process is itself sufficient to ensure the general homeostasis in the asymptotic states, as proven by several measures.

The engineered control of cellular function through the design of synthetic genetic networks is becoming plausible. Here we show how a naturally occurring network can be used as a parts list for artificial network design, and how model formulation leads to computational and analytical approaches relevant to nonlinear dynamics and statistical physics.

Dynamical criticality has been shown to enhance information processing in dynamical systems, and there is evidence for self-organized criticality in neural networks. A plausible mechanism for such self-organization is activity dependent synaptic plasticity. Here, we model neurons as discrete-state nodes on an adaptive network following stochastic dynamics. At a threshold connectivity, this system undergoes a dynamical phase transition at which persistent activity sets in. In ...

Cellular automata provide a fascinating class of dynamical systems capable of diverse complex behavior. These include simplified models for many phenomena seen in nature. Among other things, they provide insight into self-organized criticality, wherein dissipative systems naturally drive themselves to a critical state with important phenomena occurring over a wide range of length and time scales.