800 research outputs found
The complexity of dynamics in small neural circuits
Mean-field theory is a powerful tool for studying large neural networks.
However, when the system is composed of a few neurons, macroscopic differences
between the mean-field approximation and the real behavior of the network can
arise. Here we introduce a study of the dynamics of a small firing-rate network
with excitatory and inhibitory populations, in terms of local and global
bifurcations of the neural activity. Our approach is analytically tractable in
many respects, and sheds new light on the finite-size effects of the system. In
particular, we focus on the formation of multiple branching solutions of the
neural equations through spontaneous symmetry-breaking, since this phenomenon
increases considerably the complexity of the dynamical behavior of the network.
For these reasons, branching points may reveal important mechanisms through
which neurons interact and process information, which are not accounted for by
the mean-field approximation.Comment: 34 pages, 11 figures. Supplementary materials added, colors of
figures 8 and 9 fixed, results unchange
Dynamics meets Morphology: towards Dymorph Computation
In this dissertation, approaches are presented for both technically using and investigating biological principles with oscillators in the context of electrical engineering, in particular neuromorphic engineering. Thereby, dynamics as well as morphology as important neuronal principles were explicitly selected, which shape the information processing in the human brain and distinguish it from other technical systems. The aspects and principles selected here are adaptation during the encoding of stimuli, the comparatively low signal transmission speed, the continuous formation and elimination of connections, and highly complex, partly chaotic, dynamics. The selection of these phenomena and properties has led to the development of a sensory unit that is capable of encoding mechanical stress into a series of voltage pulses by the use of a MOSFET augmented by AlScN. The circuit is based on a leaky integrate and fire neuron model and features an adaptation of the pulse frequency. Furthermore, the slow signal transmission speed of biological systems was the motivation for the investigation of a temporal delay in the feedback of the output pulses of a relaxation oscillator. In this system stable pulse patterns which form due to so-called jittering bifurcations could be observed. In particular, switching between different stable pulse patterns was possible to induce. In the further course of the work, the first steps towards time-varying coupling of dynamic systems are investigated. It was shown that in a system consisting of dimethyl sulfoxid and zinc acetate, oscillators can be used to force the formation of filaments. The resulting filaments then lead to a change in the dynamics of the oscillators. Finally, it is shown that in a system with chaotic dynamics, the extension of it with a memristive device can lead to a transient stabilisation of the dynamics, a behaviour that can be identified as a repeated pass of Hopf bifurcations
Investigating the role of fast-spiking interneurons in neocortical dynamics
PhD ThesisFast-spiking interneurons are the largest interneuronal population in neocortex. It is
well documented that this population is crucial in many functions of the neocortex by
subserving all aspects of neural computation, like gain control, and by enabling
dynamic phenomena, like the generation of high frequency oscillations. Fast-spiking
interneurons, which represent mainly the parvalbumin-expressing, soma-targeting
basket cells, are also implicated in pathological dynamics, like the propagation of
seizures or the impaired coordination of activity in schizophrenia. In the present thesis,
I investigate the role of fast-spiking interneurons in such dynamic phenomena by using
computational and experimental techniques.
First, I introduce a neural mass model of the neocortical microcircuit featuring divisive
inhibition, a gain control mechanism, which is thought to be delivered mainly by the
soma-targeting interneurons. Its dynamics were analysed at the onset of chaos and
during the phenomena of entrainment and long-range synchronization. It is
demonstrated that the mechanism of divisive inhibition reduces the sensitivity of the
network to parameter changes and enhances the stability and
exibility of oscillations.
Next, in vitro electrophysiology was used to investigate the propagation of activity in
the network of electrically coupled fast-spiking interneurons. Experimental evidence
suggests that these interneurons and their gap junctions are involved in the propagation
of seizures. Using multi-electrode array recordings and optogenetics, I investigated the
possibility of such propagating activity under the conditions of raised extracellular K+
concentration which applies during seizures. Propagated activity was recorded and the
involvement of gap junctions was con rmed by pharmacological manipulations.
Finally, the interaction between two oscillations was investigated. Two oscillations with di erent frequencies were induced in cortical slices by directly activating the pyramidal
cells using optogenetics. Their interaction suggested the possibility of a coincidence
detection mechanism at the circuit level. Pharmacological manipulations were used to
explore the role of the inhibitory interneurons during this phenomenon. The results,
however, showed that the observed phenomenon was not a result of synaptic activity.
Nevertheless, the experiments provided some insights about the excitability of the
tissue through scattered light while using optogenetics.
This investigation provides new insights into the role of fast-spiking interneurons in the
neocortex. In particular, it is suggested that the gain control mechanism is important
for the physiological oscillatory dynamics of the network and that the gap junctions
between these interneurons can potentially contribute to the inhibitory restraint during
a seizure.Wellcome Trust
Understanding Epileptiform After-Discharges as Rhythmic Oscillatory Transients
Electro-cortical activity in patients with epilepsy may show abnormal
rhythmic transients in response to stimulation. Even when using the same
stimulation parameters in the same patient, wide variability in the duration of
transient response has been reported. These transients have long been
considered important for the mapping of the excitability levels in the
epileptic brain but their dynamic mechanism is still not well understood.
To understand the occurrence of abnormal transients dynamically, we use a
thalamo-cortical neural population model of epileptic spike-wave activity and
study the interaction between slow and fast subsystems.
In a reduced version of the thalamo-cortical model, slow wave oscillations
arise from a fold of cycles (FoC) bifurcation. This marks the onset of a region
of bistability between a high amplitude oscillatory rhythm and the background
state. In vicinity of the bistability in parameter space, the model has
excitable dynamics, showing prolonged rhythmic transients in response to
suprathreshold pulse stimulation. We analyse the state space geometry of the
bistable and excitable states, and find that the rhythmic transient arises when
the impending FoC bifurcation deforms the state space and creates an area of
locally reduced attraction to the fixed point. This area essentially allows
trajectories to dwell there before escaping to the stable steady state, thus
creating rhythmic transients. In the full thalamo-cortical model, we find a
similar FoC bifurcation structure.
Based on the analysis, we propose an explanation of why stimulation induced
epileptiform activity may vary between trials, and predict how the variability
could be related to ongoing oscillatory background activity.Comment: http://journal.frontiersin.org/article/10.3389/fncom.2017.00025/ful
Optimal self-induced stochastic resonance in multiplex neural networks: electrical versus chemical synapses
Electrical and chemical synapses shape the dynamics of neural networks and
their functional roles in information processing have been a longstanding
question in neurobiology. In this paper, we investigate the role of synapses on
the optimization of the phenomenon of self-induced stochastic resonance in a
delayed multiplex neural network by using analytical and numerical methods. We
consider a two-layer multiplex network, in which at the intra-layer level
neurons are coupled either by electrical synapses or by inhibitory chemical
synapses. For each isolated layer, computations indicate that weaker electrical
and chemical synaptic couplings are better optimizers of self-induced
stochastic resonance. In addition, regardless of the synaptic strengths,
shorter electrical synaptic delays are found to be better optimizers of the
phenomenon than shorter chemical synaptic delays, while longer chemical
synaptic delays are better optimizers than longer electrical synaptic delays --
in both cases, the poorer optimizers are in fact worst. It is found that
electrical, inhibitory, or excitatory chemical multiplexing of the two layers
having only electrical synapses at the intra-layer levels can each optimize the
phenomenon. And only excitatory chemical multiplexing of the two layers having
only inhibitory chemical synapses at the intra-layer levels can optimize the
phenomenon. These results may guide experiments aimed at establishing or
confirming the mechanism of self-induced stochastic resonance in networks of
artificial neural circuits, as well as in real biological neural networks.Comment: 24 pages, 7 figure
Mechanisms explaining transitions between tonic and phasic firing in neuronal populations as predicted by a low dimensional firing rate model
Several firing patterns experimentally observed in neural populations have
been successfully correlated to animal behavior. Population bursting, hereby
regarded as a period of high firing rate followed by a period of quiescence, is
typically observed in groups of neurons during behavior. Biophysical
membrane-potential models of single cell bursting involve at least three
equations. Extending such models to study the collective behavior of neural
populations involves thousands of equations and can be very expensive
computationally. For this reason, low dimensional population models that
capture biophysical aspects of networks are needed.
\noindent The present paper uses a firing-rate model to study mechanisms that
trigger and stop transitions between tonic and phasic population firing. These
mechanisms are captured through a two-dimensional system, which can potentially
be extended to include interactions between different areas of the nervous
system with a small number of equations. The typical behavior of midbrain
dopaminergic neurons in the rodent is used as an example to illustrate and
interpret our results.
\noindent The model presented here can be used as a building block to study
interactions between networks of neurons. This theoretical approach may help
contextualize and understand the factors involved in regulating burst firing in
populations and how it may modulate distinct aspects of behavior.Comment: 25 pages (including references and appendices); 12 figures uploaded
as separate file
- …