Cell-Cell Interactions: How Coupled Boolean Networks Tend to Criticality.

Biological cells are usually operating in conditions characterized by intercellular signaling and interaction, which are supposed to strongly influence individual cell dynamics. In this work, we study the dynamics of interacting random Boolean networks, focusing on attractor properties and response to perturbations. We observe that the properties of isolated critical Boolean networks are substantially maintained also in interaction settings, while interactions bias the dynamics of chaotic and ordered networks toward that of critical cells. The increase in attractors observed in multicellular scenarios, compared to single cells, allows us to hypothesize that biological processes, such as ontogeny and cell differentiation, leverage interactions to modulate individual and collective cell responses.

Sensory-Motor Loop Adaptation in Boolean Network Robots.

Recent technological advances have made it possible to produce tiny robots equipped with simple sensors and effectors. Micro-robots are particularly suitable for scenarios such as exploration of hostile environments, and emergency intervention, e.g., in areas subject to earthquakes or fires. A crucial desirable feature of such a robot is the capability of adapting to the specific environment in which it has to operate. Given the limited computational capabilities of a micro-robot, this property cannot be achieved by complicated software but it rather should come from the flexibility of simple control mechanisms, such as the sensory-motor loop. In this work, we explore the possibility of equipping simple robots controlled by Boolean networks with the capability of modulating their sensory-motor loop such that their behavior adapts to the incumbent environmental conditions. This study builds upon the cybernetic concept of homeostasis, which is the property of maintaining essential parameters inside vital ranges, and analyzes the performance of adaptive mechanisms intervening in the sensory-motor loop. In particular, we focus on the possibility of maneuvering the robot's effectors such that both their connections to network nodes and environmental features can be adapted. As the actions the robot takes have a feedback effect to its sensors mediated by the environment, this mechanism makes it possible to tune the sensory-motor loop, which, in turn, determines the robot's behavior. We study this general setting in simulation and assess to what extent this mechanism can sustain the homeostasis of the robot. Our results show that controllers made of random Boolean networks in critical and chaotic regimes can be tuned such that their homeostasis in different environments is kept. This outcome is a step towards the design and deployment of controllers for micro-robots able to adapt to different environments.

On the Criticality of Adaptive Boolean Network Robots.

Systems poised at a dynamical critical regime, between order and disorder, have been shown capable of exhibiting complex dynamics that balance robustness to external perturbations and rich repertoires of responses to inputs. This property has been exploited in artificial network classifiers, and preliminary results have also been attained in the context of robots controlled by Boolean networks. In this work, we investigate the role of dynamical criticality in robots undergoing online adaptation, i.e., robots that adapt some of their internal parameters to improve a performance metric over time during their activity. We study the behavior of robots controlled by random Boolean networks, which are either adapted in their coupling with robot sensors and actuators or in their structure or both. We observe that robots controlled by critical random Boolean networks have higher average and maximum performance than that of robots controlled by ordered and disordered nets. Notably, in general, adaptation by change of couplings produces robots with slightly higher performance than those adapted by changing their structure. Moreover, we observe that when adapted in their structure, ordered networks tend to move to the critical dynamical regime. These results provide further support to the conjecture that critical regimes favor adaptation and indicate the advantage of calibrating robot control systems at dynamical critical states.

The Impact of Self-Loops on Boolean Networks Attractor Landscape and Implications for Cell Differentiation Modelling.

Boolean networks are a notable model of gene regulatory networks and, particularly, prominent theories discuss how they can capture cellular differentiation processes. One frequent motif in gene regulatory networks, especially in those circuits involved in cell differentiation, is autoregulation. In spite of this, the impact of autoregulation on Boolean network attractor landscape has not yet been extensively discussed in literature. In this paper we propose to model autoregulation as self-loops, and analyse how the number of attractors and their robustness may change once they are introduced in a well-known and widely used Boolean networks model, namely random Boolean networks. Results show that self-loops provide an evolutionary advantage in dynamic mechanisms of cells, by increasing both number and maximal robustness of attractors. These results provide evidence to the hypothesis that autoregulation is a straightforward functional component to consolidate cell dynamics, mainly in differentiation processes.