• bursting dynamics
• complex systems
• cultured neurons
• entorhinal cortex
• Hodgkin-Huxley model
• Nonlinear Dynamics
• self-organized criticality

In the present work we investigate the dynamics of the electrical activity generated
in cultured neural networks. This research work was carried out in collaboration with
the Bio@SNS laboratory at the Institute of Biophysics of CNR in Pisa. More specifically,
the in-vitro neural networks investigated in this work are the MiBi cultures, which are
represented by neurons of the entorhinal cortex.
Our current knowledge of the relationship between the level of maturation of such
cultured neurons and the dynamics produced by the generated electrical activity is very
poor. Therefore, one of the main goals of the present work is to understand the basic
mechanisms, driving the generation of the electrical activity patterns exhibited by neural
networks, along with the role played by excitatory and inhibitory neurons. Aiming to do
so, we develop an in-silico mathematical model which allows us to simulate the neural
populations and compare our results with the corresponding experimental data.
Each neuron consists of a single compartment and is described by a Hodgkin-Huxley
mathematical model, with its specific biophysical properties. Our first step in this direc-
tion consists of understanding the basic biophysical mechanisms that drive the dynamical
behaviour of the artificial neural network. Therefore, we start with the investigation of
the mathematical properties of an individual neuron model in the network, either py-
ramidal or interneuron. To this aim, we perform a detailed bifurcation analysis of the
corresponding steady states, thus gaining useful information on the dynamical mechani-
sms responsible for the onset of self-sustained oscillations (neuron periodic firing). Next,
we investigate the network’s dynamics, where now neurons are coupled via appropriate
synapses (AMPA and GABA). To do so, we initially investigate simple models of neural
networks with all-to-all coupling. This allows us to understand which firing patterns can
be generated, along with identifying the most relevant parameters in determining the
emergence of a variety of dynamical regimes. The dynamical system under investigation
is very complex and of high dimensionality, therefore we adopt different indicators, such
as inter-spike interval, firing rate, correlation, etc. to characterize the properties of the ob-
served dynamical behaviours. Our results indicate that neural network models are clearly
able to generate a big variety of firing regimes (network bursts, high (or low) level of
synchronization firing), depending on the specific condition on the coupling parameters’
values.
In addition, we are also able to analyze the firing activity of in-vitro neural culture by
adopting a high-resolution multielectrode array (MEA) apparatus, which permits to get
high-frequency (up to 20K Hz) recordings of neurons’ extracellular potentials. From MEA
electrical activity data, making use of an appropriate algorithms, we extract neurons’
firing times. The inspection of these data show that neurons exhibit network bursting
regimes, as predicted by the neural network model simulations. Furthermore, the analysis
of neuronal avalanches allows us to observe features of self-organized criticality (SOC) in
our dynamical regime. In addition, further studies are conducted to understand how
1
signals propagate across the network.
The results obtained from our preliminary studies on a simplified neuronal network
model were employed to build more realistic mathematical models. In particular, we
adopt a step-by-step approach to improve the capability of our neural network model
to reproduce experimental results, both qualitatively and quantitatively. Initially we
introduce the noise in the model, then, as a second step, we implement local connections.
This leads to detect the emergence of signal propagation within the network model, as
observed in the experimental setting. Subsequently, we modify the density of neurons
in specific regions of the network in order to mimic both non-uniform and clustered
distributions, as observed in real cultures. The introduction of spatial inhomogeneities
into the model promoted the generation of network bursting dynamics, very similar to
the ones observed in the corresponding experimental recordings.
Our results show that many of the dynamical features of the electrical activity gene-
rated by the biological network are successfully reproduced by the in-silico mathematical
model, and more specifically signal propagation, centers of activation of network bursts,
self-organized criticality, and so on.
This work represents a first step towards our understanding of the dynamical beha-
viours of cultured neural networks. It opens up future perspectives, such as the investiga-
tion of mechanisms like synaptic reinforcement, aiming to gain a deeper insight into the
processes underlying memory and learning.