Functional connectivity in in vitro neuronal assemblies

Abstract

Complex network topologies represent the necessary substrate to support complex brain functions. In this work, we reviewed in vitro neuronal networks coupled to Micro-Electrode Arrays (MEAs) as biological substrate. Networks of dissociated neurons developing in vitro and coupled to MEAs, represent a valid experimental model for studying the mechanisms governing the formation, organization and conservation of neuronal cell assemblies. In this review, we present some examples of the use of statistical Cluster Coefficients and Small World indices to infer topological rules underlying the dynamics exhibited by homogeneous and engineered neuronal networks.

Keywords: correlation; functional connectivity; graph theory; in vitro; micro-electrode arrays; neuronal network dynamics.

Figure 1

MEA and extracellular signals. (A) The activity of a cortical neural network (28 DIVs) presents a mix of bursting and spiking activity (top). Applying a spike detection algorithm, time series are converted into a serial point process (bottom). (B,C) Examples of Micro-Electrode Arrays (MEAs) made up of (B) 60, (C) 4096 electrodes.

Figure 2

Basic graph measures and network structures. (A) Node degree is the number of connections of a given node; this panel shows a simple network divided in four different modules: Module 1, in which we can see a high-connected unit called hub, and Module 2, that presents a low connectivity case. Modules 3 and 4 show two units with high and low values of Cluster Coefficient respectively, and an example of shortest path length; the nodes X and Y are connected by the shortest possible path (three links), and two different units that we call intermediaries. (B) Classification of the network structure [scale-free (a), regular (b), small-world (c), and random (d)] and corresponding degree distributions.

Figure 3

Classification of the neural network connections. (A) Structural connectivity. (B) Functional connectivity. (C) Effective connectivity.

Figure 4

Sketches of different in vitro neuronal assemblies. (A) A homogeneous network in which neurons are free to connect without any chemical/mechanical constraint. (B) Interconnected neuronal networks. Left, two small populations are connected by means of a few number of links. Right, patterned networks where each node can be a small or large number of neurons.

Figure 5

Structural-functional connectivity analysis on high-density (HD) MEA. (A) Fluorescence image of a neural culture on the HD-MEA and a zoom at the single neuron level. (B) Functional links superimposed on a fluorescence image of a HD-MEA chip. White squares indicate the neurons more strongly connected, while white and red branches represent the links among the identified neurons (Adapted from Maccione et al., 2012). (C) Structural connectivity graph reconstructed using imaging methods combined with the functional connectivity graph obtained by Cross-Correlation analysis to obtain a refined functional connectivity graph (Adapted from Ullo et al., 2014).

Figure 6

Topological network properties during development. (A) Organization of the network structure at different stages of development (DIV: 14, 21, 28, 35). (B) Average Path Length (blue line), Average Cluster Coefficient (red line) and Small-Worldness curve (green line); the increase of the small-worldness curve during development, evaluated as (C_real/C_lattice)/(L_real/L_rand), shows a significant reorganization of the network (p < 0.05), from a random structure to a small-world architecture (Adapted from Downes et al., 2012). (C) Functional connectivity during the first 4 weeks in vitro; the hubs (black and yellow dots) promote the small-world topology; the number and the connection degree of the hubs increase during development. (D) Small-Worldness decreases with network density from 10 to 30 (DIV 28), but increases during the first 4 weeks in vitro (Adapted from Schroeter et al., 2015).

Figure 7

Examples of engineered neuronal networks. (A) left, Example of a bio-patterned network aligned with the electrode array; middle, two examples of functional connectivity maps relative to a homogeneous (black) and a patterned (red) network; right, average link length and mean path length for homogeneous (black) and patterned (red) cultures as a function of the number of strongest links (Adapted from Marconi et al., 2012). (B) Two examples of patterned networks realized with a micro-drop delivery system; bottom-left, connectivity map governing the connectivity of this patterned network; right, PSTH maps relative to one experimental (top), and one simulated phase (bottom) (Adapted from Macis et al., ; Massobrio and Martinoia, 2008). (C) Cortical–thalamic co-culture plated in a dual compartment device (cortical cells and thalamic cells are highlighted with red and green fluorescence staining, respectively). Middle, two examples of functional connectivity maps related to a cortical-thalamic system. Red, green, and blue links refer to cortical-cortical, thalamic-thalamic, and cortical-thalamic connections, respectively. Right distribution of the inter-cluster connection in a cortical-thalamic system (Adapted from Kanagasabapathi et al., 2012).

Figure 8

Effective and functional connectivity analysis. (A) PSTHs showed a network synaptic potentiation during evoked responses after the tetanus delivery (black and red lines indicate the phases before and after tetanus, respectively). (B) Map of the effective connections: a huge increase of the connections (red and black links correspond to the post- and pre-tetanus connections respectively) was found between pre- and post-tetanus phases, explaining the potentiation effect of the network. (C) Emergence of a random structure during spontaneous activity, the histogram shows the low SM index values evaluated for three different stimulation protocols (tetanic stimulation without (ST) or with a 0.2 Hz low-frequency (IN) in phase or 1 Hz iso-frequential (ISO) co-activation, inset) and for each recording phases (A,B Adapted from Chiappalone et al., 2008).