Criticality and its effect on other cortical phenomena

Neuronal avalanches are a cortical phenomenon defined by bursts of neuronal firing encapsulated by periods of quiescence. It has been found both in vivo and in vitro that neuronal avalanches follow a power law distribution which is indicative of the system being within or near a critical state. A system is critical if it is poised between order and disorder with the possibility of minor event leading to a large chain reaction. This is also observed by the system exhibiting a diverging correlation length between its components as it approaches the critical point. It has been shown that neuronal criticality is a scale-free phenomenon observed throughout the entire system as well as within each module of the system. At a small scale, neuronal networks produce avalanches which conform to power law-like distributions. At a larger scale, we observe that these systems consist of modules exhibiting long-range temporal correlations identifiable via Detrended Fluctuation Analysis (DFA). This phenomenon is hypothesised to affect network behaviour with regards to information processing, information storage, computational power, and stability - The Criticality Hypothesis. This thesis attempts to better understand critical neuronal networks and how criticality may link with other neuronal phenomena. This work begins by investigating the interplay of network connectivity, synaptic plasticity, and criticality. Using different network construction algorithms, the thesis demonstrates that Hebbian learning and Spike Timing Dependent Plasticity (STDP) robustly drive small networks towards a critical state. Moreover the thesis shows that, while the initial distribution of synaptic weights plays a significant role in attaining criticality, the network's topology at the modular level has little or no impact. Using an expanded eight-module oscillatory spiking neural network the thesis then shows the link between the different critical markers we use when attempting to observe critical behaviour at different scales. The findings demonstrate that modules exhibiting power law-like behaviour also demonstrate long-range temporal correlations throughout the system. Furthermore, we show that when modules no longer exhibit power law-like behaviour we find that they become uncorrelated or noisy. This shows a correlation between power law-like behaviour observed within each module and the long-range temporal correlations between the modules. The thesis concludes by demonstrating how criticality may be linked with other related phenomena, namely metastability and dynamical complexity. Metastability is a global property of neuronal populations that migrate between attractor-like states. Metastability can be quantified by the variance of synchrony, a measure that has been hypothesised to capture the varying influence neuronal populations have over one another and the system as a whole. The thesis shows a correlation between critical behaviour and metastability where the latter is most reliably maximised only when the former is near the critical state. This conclusion is expected as metastability, similarly to criticality reflects the interplay between the integrating and segregating tendencies of the system components. Agreeing with previous findings this suggests that metastable dynamics may be another marker of critical behaviour. A neural system is said to exhibit dynamical complexity if a balance of integrated and segregated activity occurs within the system. A common attribute of critical systems is a balance between excitation and inhibition. The final part of the thesis attempts to understand how criticality may be linked with dynamical complexity. This work shows a possible connection between these phenomena providing a foundation for further analysis. The thesis concludes with a discussion of the significant role criticality plays in determining the behaviour of neuronal networks.Open Acces