Development of input connections in neural cultures

Abstract

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 m0, the number of activated inputs needed to excite the neuron. For m0 Ӎ 15 we find that hippocampal neurons have on average Ϸ60 -120 inputs, whereas cortical neurons have Ϸ75-150, depending on neuronal density. The ratio of excitatory to inhibitory neurons is determined by using the GABAA 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 Ϸ30% of the neurons in the culture whereas for cortical cultures they are Ϸ20%. Such detailed global information on the connectivity of networks in neuronal cultures is at present inaccessible by any electrophysiological or other technique.neural network ͉ network connectivity ͉ inhibition ͉ graph theory ͉ percolation T he formation of the brain is one of the most complicated processes during development. The neural connectivity that initially emerges is organized but imprecise, and further refinement is needed for the accurate formation of the neural circuits. This requires the presence of neural activity (1), first in the form of large-scale spontaneous activity (2), and later driven by sensory experience (3, 4). The connectivity must be flexible enough to allow complex refinement, yet robust enough to sustain synchronous patterns of activity across hundreds of neurons. The formation of connectivity during maturation of the nervous system thus naturally arises as an intriguing issue. Neural cultures have been very useful as model systems to study such spontaneous activity mechanisms (5-7), persistent activity (8) and connectivity in neural networks (9, 10).Unraveling neural connectivity, however, is a daunting task; even a small culture with Ϸ10 5 neurons has several million connections. Electrophysiological approaches combined with microscopy and three-dimensional reconstructions (11, 12) have an enormous capability for identifying the connections between any two neurons, and even all of the connections of a single neuron. However, the identification of the statistical properties of the full connection distribution is beyond current capabilities. Monitoring the development of these connections in embryonic stages is even more ambitious, because it serves to link the stages of growth in the culture with those in the brain (13).We have recently developed a global bath excitation protocol coupled with graph and percolation concepts (14) to extract many properties of the network...

Network synchronization in hippocampal neurons

“…Our picture of the bursting network activity at elevated calcium is based on the idea that without blockers, a background of spontaneous synaptic activity exists and makes the neurons slightly more excitable. We have shown previously that under these conditions of strong connectivity, firing of a small fraction of the neurons, presumably those neurons that are more sensitive to inputs and lead the activity, suffices to ignite the rest of the network (28)(29)(30). An additional effect of increased network synchronization with elevated [Ca 2+ ] o was recently reported in cortical slices (31), but through differential sensitivity of excitatory and inhibitory synapses to calcium.…”

Heterogeneousk-core versus bootstrap percolation on complex networks

“…Results on non tree-like graphs have been largely numerical [24,25], although some analytic results incorporating clustering have recently been obtained [26,27]. At the same time, bootstrap percolation has emerged as a useful model for a variety of applications such as neuronal activity [28][29][30], jamming and rigidity transitions and glassy dynamics [31,32], and magnetic systems [33]. In bootstrap percolation, a set of seed vertices is initially activated, and other vertices become active if they have k active neighbors.…”

BDNF and NT-3 Increase Velocity of Activity Front Propagation in Unidimensional Hippocampal Cultures

“…Direct values for and = cannot be obtained due to the uncertainty in the value of m 0 ϭ V T /g s . Although m 0 is the same for treated and untreated cultures, and on the order of 15 (Feinerman et al 2005;Golomb and Ermentrout 1999;Jacobi and Moses 2007;Osan and Ermentrout 2002;Soriano et al 2008), its precise value is unknown.…”

“…We also studied the response of neurons to partial blocking of the synapses and used the fraction c of active receptors, given by 1/(1 ϩ [CNQX]/K d ), as a measure of the synaptic efficacy (Jacobi et al 2009;Soriano et al 2008), where [CNQX] is the concentration of the AMPA antagonist and K d ϭ 300 nM is its dissociation constant (Honore et al 1988). c varies between 0 (full blocking) and 1 (no blocking).…”