Modular architecture facilitates noise-driven control of synchrony in neuronal networks.

High-level information processing in the mammalian cortex requires both segregated processing in specialized circuits and integration across multiple circuits. One possible way to implement these seemingly opposing demands is by flexibly switching between states with different levels of synchrony. However, the mechanisms behind the control of complex synchronization patterns in neuronal networks remain elusive. Here, we use precision neuroengineering to manipulate and stimulate networks of cortical neurons in vitro, in combination with an in silico model of spiking neurons and a mesoscopic model of stochastically coupled modules to show that (i) a modular architecture enhances the sensitivity of the network to noise delivered as external asynchronous stimulation and that (ii) the persistent depletion of synaptic resources in stimulated neurons is the underlying mechanism for this effect. Together, our results demonstrate that the inherent dynamical state in structured networks of excitable units is determined by both its modular architecture and the properties of the external inputs.

The broad edge of synchronization: Griffiths effects and collective phenomena in brain networks.

Many of the amazing functional capabilities of the brain are collective properties stemming from the interactions of large sets of individual neurons. In particular, the most salient collective phenomena in brain activity are oscillations, which require the synchronous activation of many neurons. Here, we analyse parsimonious dynamical models of neural synchronization running on top of synthetic networks that capture essential aspects of the actual brain anatomical connectivity such as a hierarchical-modular and core-periphery structure. These models reveal the emergence of complex collective states with intermediate and flexible levels of synchronization, halfway in the synchronous-asynchronous spectrum. These states are best described as broad Griffiths-like phases, i.e. an extension of standard critical points that emerge in structurally heterogeneous systems. We analyse different routes (bifurcations) to synchronization and stress the relevance of 'hybrid-type transitions' to generate rich dynamical patterns. Overall, our results illustrate the complex interplay between structure and dynamics, underlining key aspects leading to rich collective states needed to sustain brain functionality. This article is part of the theme issue 'Emergent phenomena in complex physical and socio-technical systems: from cells to societies'.

Jensen's force and the statistical mechanics of cortical asynchronous states.

Cortical networks are shaped by the combined action of excitatory and inhibitory interactions. Among other important functions, inhibition solves the problem of the all-or-none type of response that comes about in purely excitatory networks, allowing the network to operate in regimes of moderate or low activity, between quiescent and saturated regimes. Here, we elucidate a noise-induced effect that we call "Jensen's force" -stemming from the combined effect of excitation/inhibition balance and network sparsity- which is responsible for generating a phase of self-sustained low activity in excitation-inhibition networks. The uncovered phase reproduces the main empirically-observed features of cortical networks in the so-called asynchronous state, characterized by low, un-correlated and highly-irregular activity. The parsimonious model analyzed here allows us to resolve a number of long-standing issues, such as proving that activity can be self-sustained even in the complete absence of external stimuli or driving. The simplicity of our approach allows for a deep understanding of asynchronous states and of the phase transitions to other standard phases it exhibits, opening the door to reconcile, asynchronous-state and critical-state hypotheses, putting them within a unified framework. We argue that Jensen's forces are measurable experimentally and might be relevant in contexts beyond neuroscience.

Limited role of spatial self-structuring in emergent trade-offs during pathogen evolution.

Pathogen transmission and virulence are main evolutionary variables broadly assumed to be linked through trade-offs. In well-mixed populations, these trade-offs are often ascribed to physiological restrictions, while populations with spatial self-structuring might evolve emergent trade-offs. Here, we reexamine a spatially-explicit, SIR model of the latter kind proposed by Ballegooijen and Boerlijst with the aim of characterising the mechanisms causing the emergence of the trade-off and its structural robustness. Using invadability criteria, we establish the conditions under which an evolutionary feedback between transmission and virulence mediated by pattern formation can poise the system to a critical boundary separating a disordered state (without emergent trade-off) from a self-structured phase (where the trade-off emerges), and analytically calculate the functional shape of the boundary in a certain approximation. Beyond evolutionary parameters, the success of an invasion depends on the size and spatial structure of the invading and invaded populations. Spatial self-structuring is often destroyed when hosts are mobile, changing the evolutionary dynamics to those of a well-mixed population. In a metapopulation scenario, the systematic extinction of the pathogen in the disordered phase may counteract the disruptive effect of host mobility, favour pattern formation and therefore recover the emergent trade-off.