Neuronal avalanches in Watts-Strogatz networks of stochastic spiking neurons

Neuronal avalanche dynamics regulated by spike-timing-dependent plasticity under different topologies and heterogeneities

Neuronal avalanches, a critical state of network self-organization, have been widely observed in electrophysiological records at different signal levels and spatial scales of the brain, which has significant influence on information transmission and processing in the brain. In this paper, the collective behavior of neuron firing is studied based on Leaky Integrate-and-Fire model and we induce spike-timing-dependent plasticity (STDP) to update the connection weight through competition between adjacent neurons in different network topologies. The result shows that STDP can facilitate the synchronization of the network and increase the probability of large-scale neuron avalanche obviously. Moreover, both the structure of STDP and network connection density can affect the generation of avalanche critical states, specifically, learning rate has positive correlation effect on the slope of power-law distribution and time constant has negative correction on it. However, when we the increase of heterogeneity in network, STDP can only has obvious promotion in synchrony under suitable level of heterogeneity. And we find that the process of long-term potentiation is sensitive to the adjustment of time constant and learning rate, unlike long-term depression, which is only sensitive to learning rate in heterogeneity network. It is suggested that presented results could facilitate our understanding on synchronization in various neural networks under the effect of STDP learning rules.

How network structure affects the dynamics of a network of stochastic spiking neurons

Up to now, it still remains an open question about the relation between the structure of brain networks and their functions. The effects of structure on the dynamics of neural networks are usually investigated via extensive numerical simulations, while analytical analysis is always very difficult and thus rare. In this work, we explored the effects of a random regular graph on the dynamics of a neural network of stochastic spiking neurons, which has a bistable region when fully connected. We showed by numerical simulations that as the number of each neuron's neighbors decreases, the bistable region shrinks and eventually seems to disappear, and a critical-like transition appears. In the meantime, we made analytical analysis that explains numerical results. We hope this would give some insights into how structure affects the dynamics of neural networks from a theoretical perspective, rather than merely by numerical simulations.

Self-organized collective oscillations in networks of stochastic spiking neurons

The theory of self-organized bistability (SOB) is the counterpart of self-organized criticality for systems tuning themselves to the edge of bistability of a discontinuous phase transition, rather than to the critical point of a continuous one. As far as we are concerned, there are currently few neural network models that display SOB or rather its non-conservative version, self-organized collective oscillations (SOCO). We show that by slightly modifying the firing function, a stochastic excitatory/inhibitory network model can display SOCO behaviors, thus providing some insights into how SOCO behaviors can be generated in neural network models.

Late stage of the formation of a protein corona around nanoparticles in biofluids

In biofluids containing various proteins, nanoparticles rapidly come to be surrounded by a nanometer-thick protein layer referred to as a protein corona. The late stage of this process occurs via replacement of proteins already bound to a nanoparticle by new ones. In the available kinetic models, this process is considered to include independent acts of protein detachment and attachment. It can, however, occur also at the level of protein pairs via exchange, i.e., concerted replacement of an attached protein by a newly arrived one. I argue that the exchange channel can be more important than the conventional one. To illustrate the likely specifics of the exchange channel, I present a kinetic model focused exclusively on this channel and based on the Evans-Polanyi-type relation between the activation energies of the protein-exchange steps and the protein binding energies. The corresponding kinetics were calculated for three qualitatively different distributions of proteins in solution over binding energy (with a maximum or monotonously decreasing or increasing, respectively) and are found to be similar, with relatively rapid replacement of weakly bound proteins and slow redistribution of strongly bound proteins. The ratio of the timescales characterizing the evolution of weakly and strongly bound proteins is found to depend on the type of the binding-energy distribution.

Similar local neuronal dynamics may lead to different collective behavior

This report is concerned with the relevance of the microscopic rules that implement individual neuronal activation, in determining the collective dynamics, under variations of the network topology. To fix ideas we study the dynamics of two cellular automaton models, commonly used, rather in-distinctively, as the building blocks of large-scale neuronal networks. One model, due to Greenberg and Hastings (GH), can be described by evolution equations mimicking an integrate-and-fire process, while the other model, due to Kinouchi and Copelli (KC), represents an abstract branching process, where a single active neuron activates a given number of postsynaptic neurons according to a prescribed "activity" branching ratio. Despite the apparent similarity between the local neuronal dynamics of the two models, it is shown that they exhibit very different collective dynamics as a function of the network topology. The GH model shows qualitatively different dynamical regimes as the network topology is varied, including transients to a ground (inactive) state, continuous and discontinuous dynamical phase transitions. In contrast, the KC model only exhibits a continuous phase transition, independently of the network topology. These results highlight the importance of paying attention to the microscopic rules chosen to model the interneuronal interactions in large-scale numerical simulations, in particular when the network topology is far from a mean-field description. One such case is the extensive work being done in the context of the Human Connectome, where a wide variety of types of models are being used to understand the brain collective dynamics.