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Register a new userSimple model of complex dynamics of activity patterns in developing networks of neuronal cultures
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Living neuronal networks in dissociated neuronal cultures are widely known for their ability to generate highly robust spatiotemporal activity patterns in various experimental conditions. These include neuronal avalanches satisfying the power scaling law and thereby exemplifying self-organized criticality in living systems. A crucial question is how these patterns can be explained and modeled in a way that is biologically meaningful, mathematically tractable and yet broad enough to account for neuronal heterogeneity and complexity. Here we propose a simple model which may offer an answer to this question. Our derivations are based on just few phenomenological observations concerning input-output behavior of an isolated neuron. A distinctive feature of the model is that at the simplest level of description it comprises of only two variables, a network activity variable and an exogenous variable corresponding to energy needed to sustain the activity and modulate the efficacy of signal transmission. Strikingly, this simple model is already capable of explaining emergence of network spikes and bursts in developing neuronal cultures. The model behavior and predictions are supported by empirical observations and published experimental evidence on cultured neurons behavior exposed to oxygen and energy deprivation. At the larger, network scale, introduction of the energy-dependent regulatory mechanism enables the network to balance on the edge of the network percolation transition. Network activity in this state shows population bursts satisfying the scaling avalanche conditions. This network state is self-sustainable and represents a balance between global network-wide processes and spontaneous activity of individual elements.
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We present a study on the selection of a variety of activity patterns among neurons that are connected in multiplex framework, with neurons on two layers with different functional couplings. With Hindmarsh-Rose model for the dynamics of single neurons, we analyze the possible patterns of dynamics in each layer separately, and report emergent patterns of activity like anti-phase oscillations in multi-clusters with phase regularities and enhanced amplitude and frequency with mixed mode oscillations when the connections are inhibitory. When they are multiplexed with neurons of one layer coupled with excitatory synaptic coupling and neurons of the other layer coupled with inhibitory synaptic coupling, we observe transfer or selection of interesting patterns of collective behaviour between the layers, inducing anti-phase oscillations and multi-cluster oscillations. While the revival of oscillations occurs in the layer with excitatory coupling, the transition from anti-phase to in-phase and vice versa is observed in the other layer with inhibitory synaptic coupling. We also discuss how the selection of these patterns can be controlled by tuning the intra-layer or inter-layer coupling strengths or increasing the range of non-local coupling. With one layer having electrical coupling while the other synaptic coupling of excitatory(inhibitory)type, we find in-phase(anti-phase) synchronized patterns of activity among neurons in both layers.
A variety of physical, social and biological systems generate complex fluctuations with correlations across multiple time scales. In physiologic systems, these long-range correlations are altered with disease and aging. Such correlated fluctuations in living systems have been attributed to the interaction of multiple control systems; however, the mechanisms underlying this behavior remain unknown. Here, we show that a number of distinct classes of dynamical behaviors, including correlated fluctuations characterized by $1/f$-scaling of their power spectra, can emerge in networks of simple signaling units. We find that under general conditions, complex dynamics can be generated by systems fulfilling two requirements: i) a ``small-world topology and ii) the presence of noise. Our findings support two notable conclusions: first, complex physiologic-like signals can be modeled with a minimal set of components; and second, systems fulfilling conditions (i) and (ii) are robust to some degree of degradation, i.e., they will still be able to generate $1/f$-dynamics.
In self-organized criticality (SOC) models, as well as in standard phase transitions, criticality is only present for vanishing driving external fields $h rightarrow 0$. Considering that this is rarely the case for natural systems, such a restriction poses a challenge to the explanatory power of these models. Besides that, in models of dissipative systems like earthquakes, forest fires and neuronal networks, there is no true critical behavior, as expressed in clean power laws obeying finite-size scaling, but a scenario called dirty criticality or self-organized quasi-criticality (SOqC). Here, we propose simple homeostatic mechanisms which promote self-organization of coupling strengths, gains, and firing thresholds in neuronal networks. We show that near criticality can be reached and sustained even in the presence of external inputs because the firing thresholds adapt to and cancel the inputs, a phenomenon similar to perfect adaptation in sensory systems. Similar mechanisms can be proposed for the couplings and local thresholds in spin systems and cellular automata, which could lead to applications in earthquake, forest fire, stellar flare, voting and epidemic modeling.
Relay synchronization in complex networks is characterized by the synchronization of remote parts of the network due to their interaction via a relay. In multilayer networks, distant layers that are not connected directly can synchronize due to signal propagation via relay layers. In this work, we investigate relay synchronization of partial synchronization patterns like chimera states in three-layer networks of interacting FitzHugh-Nagumo oscillators. We demonstrate that the phenomenon of relay synchronization is robust to topological random inhomogeneities of small-world type in the layer networks. We show that including randomness in the connectivity structure either of the remote network layers, or of the relay layer, increases the range of interlayer coupling strength where relay synchronization can be observed.
Complex chemical reaction networks, which underlie many industrial and biological processes, often exhibit non-monotonic changes in chemical species concentrations, typically described using nonlinear models. Such non-monotonic dynamics are in principle possible even in linear models if the matrices defining the models are non-normal, as characterized by a necessarily non-orthogonal set of eigenvectors. However, the extent to which non-normality is responsible for non-monotonic behavior remains an open question. Here, using a master equation to model the reaction dynamics, we derive a general condition for observing non-monotonic dynamics of individual species, establishing that non-normality promotes non-monotonicity but is not a requirement for it. In contrast, we show that non-normality is a requirement for non-monotonic dynamics to be observed in the Renyi entropy. Using hydrogen combustion as an example application, we demonstrate that non-monotonic dynamics under experimental conditions are supported by a linear chain of connected components, in contrast with the dominance of a single giant component observed in typical random reaction networks. The exact linearity of the master equation enables development of rigorous theory and simulations for dynamical networks of unprecedented size (approaching $10^5$ dynamical variables, even for a network of only 20 reactions and involving less than 100 atoms). Our conclusions are expected to hold for other combustion processes, and the general theory we develop is applicable to all chemical reaction networks, including biological ones.
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