Percolation in living neural networks

Percolation transition at growing spatiotemporal fractal patterns in models of mesoscopic neural networks

Spike packet propagation is modeled in mesoscopic-scale networks, composed of locally and recurrently coupled neural pools, and embedded in a two-dimensional lattice. Site dynamics is governed by three key parameters--pool connectedness probability, synaptic strength (following the steady-state distribution of some realizations of spike-timing-dependent plasticity learning rule), and the neuron refractoriness. Formation of spatiotemporal patterns in our model, synfire chains, exhibits critical behavior, with the emerging percolation phase transition controlled by the probability for nonzero synaptic strength value. Applying the finite-size scaling method, we infer the critical probability dependence on synaptic strength and refractoriness and determine the effects of connection topology on the pertaining percolation clusters fractal dimensions. We find that the directed percolation and the pair contact process with diffusion constitute the relevant universality classes of phase transitions observed in a class of mesoscopic-scale network models, which may be related to recently reported data on in vitro cultures.

Viewing brain processes as Critical State Transitions across levels of organization: Neural events in Cognition and Consciousness, and general principles

In this theoretical and speculative essay, I propose that insights into certain aspects of neural system functions can be gained from viewing brain function in terms of the branch of Statistical Mechanics currently referred to as "Modern Critical Theory" [Stanley, H.E., 1987. Introduction to Phase Transitions and Critical Phenomena. Oxford University Press; Marro, J., Dickman, R., 1999. Nonequilibrium Phase Transitions in Lattice Models. Cambridge University Press, Cambridge, UK]. The application of this framework is here explored in two stages: in the first place, its principles are applied to state transitions in global brain dynamics, with benchmarks of Cognitive Neuroscience providing the relevant empirical reference points. The second stage generalizes to suggest in more detail how the same principles could also apply to the relation between other levels of the structural-functional hierarchy of the nervous system and between neural assemblies. In this view, state transitions resulting from the processing at one level are the input to the next, in the image of a 'bucket brigade', with the content of each bucket being passed on along the chain, after having undergone a state transition. The unique features of a process of this kind will be discussed and illustrated.

Development of input connections in neural cultures

We introduce an approach for the quantitative assessment of the connectivity in neuronal cultures, based on the statistical mechanics of percolation on a graph. This allows us to monitor the development of the culture and to see the emergence of connectivity in the network. The culture becomes fully connected at a time equivalent to the expected time of birth. The spontaneous bursting activity that characterizes cultures develops in parallel with the connectivity. The average number of inputs per neuron can be quantitatively determined in units of m(0), the number of activated inputs needed to excite the neuron. For m(0) approximately 15 we find that hippocampal neurons have on average approximately 60-120 inputs, whereas cortical neurons have approximately 75-150, depending on neuronal density. The ratio of excitatory to inhibitory neurons is determined by using the GABA(A) antagonist bicuculine. This ratio changes during development and reaches the final value at day 7-8, coinciding with the expected time of the GABA switch. For hippocampal cultures the inhibitory cells comprise approximately 30% of the neurons in the culture whereas for cortical cultures they are approximately 20%. Such detailed global information on the connectivity of networks in neuronal cultures is at present inaccessible by any electrophysiological or other technique.

Consciousness related neural events viewed as brain state space transitions

This theoretical and speculative essay addresses a categorical distinction between neural events of sensory-motor cognition and those presumably associated with consciousness. It proposes to view this distinction in the framework of the branch of Statistical Physics currently referred to as Modern Critical Theory (Stanley, Introduction to phase transitions and critical phenomena, 1987; Marro and Dickman, Nonequilibrium phase transitions in lattice, 1999). Based on established landmarks of brain dynamics, network configurations and their role for conveying oscillatory activity of certain frequencies bands, the question is examined: what kind of state space transitions can systems with these properties undergo, and could the relation between neural processes of sensory-motor cognition and those of events in consciousness be of the same category as is characterized by state transitions in non-equilibrium physical systems? Approaches for empirical validation of this view by suitably designed brain imaging studies, and for computational simulations of the proposed principle are discussed.

Magnetic stimulation of one-dimensional neuronal cultures

Transcranial magnetic stimulation is a remarkable tool for neuroscience research, with a multitude of diagnostic and therapeutic applications. Surprisingly, application of the same magnetic stimulation directly to neurons that are dissected from the brain and grown in vitro was not reported to activate them to date. Here we report that central nervous system neurons patterned on large enough one-dimensional rings can be magnetically stimulated in vitro. In contrast, two-dimensional cultures with comparable size do not respond to excitation. This happens because the one-dimensional pattern enforces an ordering of the axons along the ring, which is designed to follow the lines of the magnetically induced electric field. A small group of sensitive (i.e., initiating) neurons respond even when the network is disconnected, and are presumed to excite the entire network when it is connected. This implies that morphological and electrophysiological properties of single neurons are crucial for magnetic stimulation. We conjecture that the existence of a select group of neurons with higher sensitivity may occur in the brain in vivo as well, with consequences for transcranial magnetic stimulation.

What the training of a neuronal network optimizes

In the study a model of training of neuronal networks built of integrate-and-fire neurons is investigated. Neurons are assembled into complex networks of Watts-Strogatz type. Every neuronal network contains a single receptor neuron. The receptor neuron, stimulated by an external signal, evokes spikes in equal time intervals. The spikes generated by the receptor neuron induce subsequent activity of a whole network. The depolarization signals, traveling the network, modify synaptic couplings according to a kick-and-delay rule, whose process is termed "training." It is shown that the training decreases the mean length of paths along which a depolarization signal is transmitted from the receptor neuron. Consequently, the training also decreases the reaction time and the energy expense necessary for the network to react to the external stimulus. It is shown that the initial distribution of synaptic couplings crucially determines the performance of trained networks.