The sodium-potassium pump controls the intrinsic firing of the cerebellar Purkinje neuron

In vitro, cerebellar Purkinje cells can intrinsically fire action potentials in a repeating trimodal or bimodal pattern. The trimodal pattern consists of tonic spiking, bursting, and quiescence. The bimodal pattern consists of tonic spiking and quiescence. It is unclear how these firing patterns are generated and what determines which firing pattern is selected. We have constructed a realistic biophysical Purkinje cell model that can replicate these patterns. In this model, Na+/K+ pump activity sets the Purkinje cell's operating mode. From rat cerebellar slices we present Purkinje whole cell recordings in the presence of ouabain, which irreversibly blocks the Na+/K+ pump. The model can replicate these recordings. We propose that Na+/K+ pump activity controls the intrinsic firing mode of cerbellar Purkinje cells

Biophysics of Purkinje computation

Although others have reported and characterised different patterns of Purkinje firing (Womack and Khodakhah, 2002, 2003, 2004; McKay and Turner, 2005) this thesis is the first study that moves beyond their description and investigates the actual basis of their generation. Purkinje cells can intrinsically fire action potentials in a repeating trimodal or bimodal pattern. The trimodal pattern consists of tonic spiking, bursting and quiescence. The bimodal pattern consists of tonic spiking and quiescence. How these firing patterns are generated, and what ascertains which firing pattern is selected, has not been determined to date. We have constructed a detailed biophysical Purkinje cell model that can replicate these patterns and which shows that Na+/K+ pump activity sets the model’s operating mode. We propose that Na+/K+ pump modulation switches the Purkinje cell between different firing modes in a physiological setting and so innovatively hypothesise the Na+/K+ pump to be a computational element in Purkinje information coding. We present supporting in vitro Purkinje cell recordings in the presence of ouabain, which irreversibly blocks the Na+/K+ pump. Climbing fiber (CF) input has been shown experimentally to toggle a Purkinje cell between an up (firing) and down (quiescent) state and set the gain of its response to parallel fiber (PF) input (Mckay et al., 2007). Our Purkinje cell model captures these toggle and gain computations with a novel intracellular calcium computation that we hypothesise to be applicable in real Purkinje cells. So notably, our Purkinje cell model can compute, and importantly, relates biophysics to biological information processing. Our Purkinje cell model is biophysically detailed and as a result is very computationally intensive. This means that, whilst it is appropriate for studying properties of the 8 individual Purkinje cell (e.g. relating channel densities to firing properties), it is unsuitable for incorporation into network simulations. We have overcome this by deploying mathematical transforms to produce a simpler, surrogate version of our model that has the same electrical properties, but a lower computational overhead. Our hope is that this model, of intermediate biological fidelity and medium computational complexity, will be used in the future to bridge cellular and network studies and identify how distinctive Purkinje behaviours are important to network and system function

The Effect of Input from the Cerebellar Nuclei on Activity in Thalamocortical Networks

The cerebellum is a prominent brain structure that contains more than half of all neurons, in the brain, which are densely packed and make up 15% of the total brain mass (Andersen et al., 1992). It is well known for its contribution to the control of motor functions, but it also plays a pivotal role in non-motor behaviours. The cerebellum is also involved in numerous pathological conditions. This thesis contributes to the understanding of the pathophysiology of the cerebello-thalamo-cortical pathways. I concentrate on two cerebellar diseases, namely: absence epilepsy (Noebels, 2005) and downbeat nystagmus (DBN) (Strupp et al., 2007). In this thesis the missing link in explaining the alleviating mechanism of a potassium channel blocker on downbeat nystagmus was found. A simulated single biologically detailed floccular target neuron (FTN) model was stimulated by input from cerebellar Purkinje cells (PCs). It was demonstrated that for both synchronised and unsynchronised input, irregular PC spike trains (which resembles the DBN condition) resulted in elevated FTN firing rates, in comparison with regular (4-AP treated) ones. This increase or decrease of the FTN firing rates during DBN, or after 4-AP treatment, respectively depended on short term depression (STD) at the PC - FTN synapses exclusively in the cases when the PC input was unsynchronised. In contrast, results of previous modelling studies (Glasauer et al, 2011; Glasauer and Rossert, 2008) were not in-line with the corresponding experimental findings (Alvina and Khodakhah, 2010) because they did not take into account the STD on the FTN-PC synapses. It was also demonstrated here that the cerebellar output contributes to the control of absence epilepsy that originates in the thalamocortical network. Moreover, the cerebellar input was most effective when it arrived at the peak of the GSWD burst, with the least effective input arriving during the inter-ictal interval, showing clear phase-dependency. I have also shown that a three-fold increase in the inhibitory time constant, drives the asynchronous-irregular network into an ictal state. This increase reflects the GABAA block. A change to GABAB dominated inhibition results in GSWDs, in which the “wave” component is related to the slow GABAB-mediated K+ currents (Destexhe, 1998). Therefore, in this thesis two important contributions are made to the understanding of cerebellar pathological states: absence epilepsy and DBN, which might in turn be useful in the potential treatment of these conditions.

Generation of the complex spike in cerebellar Purkinje cells.

Each neuron of the nervous system is a machine specialised to appropriately transform its synaptic inputs into a pattern of spiking output. This is achieved through the combination of specialisations in synaptic properties and location, passive cell geometry and placement of particular active ion channels. The challenge presented to the neuroscientist is to, within each cell type, identify such specialisations in input distribution and resulting active events, and assess their relative importance in the generation of action potential output patterns. The Purkinje cell, in particular its response to climbing fibre (CF) input, is an excellent setting in which to attempt to meet this challenge. The Purkinje cell receives a single, easily isolated CF axon, which makes hundreds of synapses across the cell's highly branched, active dendritic tree, resulting in the generation of prominent dendritic calcium spikes and a distinctive, reproducible burst of fast action potentials (the complex spike) at the soma. In this thesis I have separated out the importance of the size of this input, its location and the active dendritic spikes it triggers in the generation of the complex spike. I have found that, to a large extent, the complex spike pattern is determined by the size of the CF input alone. I have characterised the complex spike (its number of spikes, their timing, height and reliability) at both constant physiological frequency and across a range of paired- pulse depression causing intervals. By alternating between whole cell current and voltage clamp in the same cell, I have recorded both the complex spikes and EPSCs generated at certain paired pulse intervals. In this way I have been able to construct the EPSC - complex spike 'input - output' relationship. This demonstrated that there is a straightforward linear transformation between the EPSC input amplitude and the number and timing of spikes in the complex spike. This applies across cells, explaining a large amount of the inter-cell variability in complex spike pattern. Input location and dendritic spikes have surprisingly little influence over the Purkinje cell complex spike. I found that complex spikes generated by dendritically distributed CF input can be reproduced by using conductance clamp to inject CF-like synaptic conductance at the soma. Both CF input and somatic EPSG injection produced complex spike waveforms that can only be easily explained by a model in which spikelets are initiated at a distant site and variably propagated to the soma. By using simultaneous somatic and dendritic recording I have demonstrated that this distant site initiation site is not in the dendrites. Somatic EPSG injection reproduced complex spikes independently of dendritic spikes, and extra dendritic spikes triggered by CF stimulation were associated with only 0.24 0.09 extra somatic spikelets in the complex spike. Rather, I have found that dendritic spikes, generated reliably by the dendritic location of CF inputs, have a role in regulating the post-complex spike pause. An extra dendritic spike generates a 3.4 0.7 mV deeper AHP and a 52 11 % longer pause before spontaneous spiking resumed. In this way, I have identified specialisations that encode the size, and thus timing, of CF inputs in the complex spike burst, whilst allowing the dendritic excitation of Purkinje cells (which is strongly associated synaptic and intrinsic plasticity) to be simultaneously encoded in the post-complex spike pause. This may reflect the complex spike's proposed dual role in both controlling ongoing movement and correcting for motor errors

The Mind Agents in Netlogo 3.1

In [Houk, 2005], the “Agents of the mind” idea is proposed as a suitable framework for studying the dynamics and complexities of mind. “Agents of the mind” is inspired by the society of mind idea of Marvin Minsky [Minsky, 1988]. According to the society of mind, the mind is a complex system. The mind agents are elusive to identify. The mind is proposed as a hierarchy of agents. The higher hierarchy agents compose of lower hierarchy agents. Higher level agents do not command lower level agents but they basically trigger or invoke lower level agents. Agents are functional entities and they interact with each other. One important part of the society of mind idea is that agents at the lowest level are the real workers. Higher level functionalities emerge as a result of the functioning of the lower level agents and the interactions between them. In agents of the mind project, computational distributed processing modules (DPM) are posited for corresponding anatomically defined assemblies and they are referred to as the agents of the mind. M1 is an anatomical area in the cerebral cortex which produces voluntary commands via its loops through basal ganglia and cerebellum. M1-DPM is a computational distributed processing module which simulates M1 area and its loops for voluntary commands production. We use Netlogo 3.1 agent-based programming environment to illuminate the properties of mind. In this work, the attractor network in cerebellar loop and the effects of Purkinje cell on production of motor commands have been studied. The results are reported in this paper

26th Annual Computational Neuroscience Meeting (CNS*2017): Part 3 - Meeting Abstracts - Antwerp, Belgium. 15–20 July 2017

This work was produced as part of the activities of FAPESP Research,\ud Disseminations and Innovation Center for Neuromathematics (grant\ud 2013/07699-0, S. Paulo Research Foundation). NLK is supported by a\ud FAPESP postdoctoral fellowship (grant 2016/03855-5). ACR is partially\ud supported by a CNPq fellowship (grant 306251/2014-0)

Pathophysiological mechanisms of absence epilepsy: a computational modelling study

A typical absence is a non-convulsive epileptic seizure that is a sole symptom of childhood absence epilepsy (CAE). It is characterised by a generalised hyper-synchronous activity (2.5-5 Hz) of neurons in the thalamocortical network that manifests as a spike and slow-wave discharge (SWD) in the electroencephalogram. Although CAE is not a benign form of epilepsy, its physiological basis is not well understood. In an attempt to make progress regarding the mechanism of SWDs, I built a large-scale computational model of the thalamocortical network that replicated key cellular and network electric oscillatory behaviours. Model simulation indicated that there are multiple pathological pathways leading to SWDs. They fell into three categories depending on their network-level effects. Moreover, all SWDs had the same physiological mechanism of generation irrespective of their underlying pathology. They were initiated by an increase in NRT cell bursting prior to the SWD onset. SWDs critically depended on the T-type Ca2+ current (IT) mediated firing in NRT and higher-order thalamocortical relay cells (TCHO), as well as GABAB synaptic receptor-mediated IPSPs in TCHO cells. On the other hand, first-order thalamocortical cells were inhibited during SWDs and did not actively participate in their generation. These cells, however, could promote or disrupt SWD generation if they were hyperpolarised or depolarised, respectively. Importantly, only a minority of active TC cells with a small proportion of them bursting were necessary to ensure the SWD generation. In terms of their relationship to other brain rhythms, simulated SWDs were a product of NRT sleep spindle (6.5-14 Hz) and cortical δ (1-4 Hz) pacemakers and had their oscillation frequency settle between the preferred oscillation frequencies of the two pacemakers with the actual value depending on the cortical bursting intensity. These modelling results are discussed in terms of their implications for understanding CAE and its future research and treatment

Pathophysiological mechanisms of absence epilepsy: a computational modelling study

A typical absence is a non-convulsive epileptic seizure that is a sole symptom of childhood absence epilepsy (CAE). It is characterised by a generalised hyper-synchronous activity (2.5-5 Hz) of neurons in the thalamocortical network that manifests as a spike and slow-wave discharge (SWD) in the electroencephalogram. Although CAE is not a benign form of epilepsy, its physiological basis is not well understood. In an attempt to make progress regarding the mechanism of SWDs, I built a large-scale computational model of the thalamocortical network that replicated key cellular and network electric oscillatory behaviours. Model simulation indicated that there are multiple pathological pathways leading to SWDs. They fell into three categories depending on their network-level effects. Moreover, all SWDs had the same physiological mechanism of generation irrespective of their underlying pathology. They were initiated by an increase in NRT cell bursting prior to the SWD onset. SWDs critically depended on the T-type Ca2+ current (IT) mediated firing in NRT and higher-order thalamocortical relay cells (TCHO), as well as GABAB synaptic receptor-mediated IPSPs in TCHO cells. On the other hand, first-order thalamocortical cells were inhibited during SWDs and did not actively participate in their generation. These cells, however, could promote or disrupt SWD generation if they were hyperpolarised or depolarised, respectively. Importantly, only a minority of active TC cells with a small proportion of them bursting were necessary to ensure the SWD generation. In terms of their relationship to other brain rhythms, simulated SWDs were a product of NRT sleep spindle (6.5-14 Hz) and cortical δ (1-4 Hz) pacemakers and had their oscillation frequency settle between the preferred oscillation frequencies of the two pacemakers with the actual value depending on the cortical bursting intensity. These modelling results are discussed in terms of their implications for understanding CAE and its future research and treatment

Effects of ionic concentration dynamics on neuronal activity

Neuronen sind bei der Informationsübertragung des zentralen Nervensystems von entscheidender Bedeutung. Ihre Aktivität liegt der Signalverarbeitung und höheren kognitiven Prozessen zugrunde. Neuronen sind in den extrazellulären Raum eingebettet, der mehrere Teilchen, darunter auch Ionen, enthält. Ionenkonzentrationen sind nicht statisch. Intensive neuronale Aktivität kann intrazelluläre und extrazelluläre Ionenkonzentrationen verändern. In dieser Arbeit untersuche ich das Wechselspiel zwischen neuronaler Aktivität und der Dynamik der Ionenkonzentrationen. Dabei konzentriere ich mich hauptsächlich auf extrazelluläre Kalium- und intrazelluläre Natriumkonzentrationen. Mit Hilfe der Theorie dynamischer Systeme zeige ich, wie moderate Änderungen dieser Ionenkonzentrationen die neuronale Aktivität qualitativ verändern können, wodurch sich möglicherweise die Signalverarbeitung verändert. Dann modelliere ich ein leitfähigkeitsbasiertes neuronales Netzwerk mit Spikes. Das Modell sagt voraus, dass eine moderate Änderung der Konzentrationen, die einen Mikroschaltkreis von Neuronen umgeben, die Leistungsspektraldichte der Populationsaktivität verändern könnte. Insgesamt unterstreicht diese Arbeit die Bedeutung der Dynamik der Ionenkonzentrationen für das Verständnis neuronaler Aktivität auf langen Zeitskalen und liefert technische Erkenntnisse darüber, wie das Zusammenspiel zwischen ihnen modelliert und analysiert werden kann.Neurons are essential in the information transfer mechanisms of the central nervous system. Their activity underlies both basic signal processing, and higher cognitive processes. Neurons are embedded in the extracellular space, which contains multiple particles, including ions which are vital to their functioning. Ionic concentrations are not static, intense neuronal activity alters the intracellular and extracellular ionic concentrations which in turn affect neuronal functioning. In this thesis, I study the interplay between neuronal activity and ionic concentration dynamics. I focus specifically on the extracellular potassium and intracellular sodium concentrations. Using dynamical systems theory, I illustrate how moderate changes in these ionic concentrations can qualitatively change neuronal activity, potentially altering signal processing. I then model a conductance-based spiking neural network. The model predicts that a moderate change in the concentrations surrounding a microcircuit of neurons could modify the power spectral density of the population activity. Altogether, this work highlights the need to consider ionic concentration dynamics to understand neuronal activity on long time scales and provides technical insights on how to model and analyze the interplay between them

Modelling gap junction-coupled networks of olfactory bulb mitral cells

Summary of Thesis: The olfactory bulb forms the first level of input integration for olfactory receptor neurons that receive stimuli from odorant molecules in the nose. The olfactory bulb is multi channel in nature, with each channel containing its own populations of mitral cells. These channels each handle the input from neurons expressing a single type of olfactory receptor protein tuned to a unique range of odorant structures. I have constructed a mitral cell gap-junction network model with morphologically accurate mitral cells to study the behaviour of mitral cells in a channel population. The passive parameters of each of the mitral cells were determined by fitting to in vitro recordings. Sodium and potassium channels were added to the mitral cells to give the ability to generate action potentials. Gap-junctions were placed in the apical dendrite tufts of the mitral cells and their conductance adjusted to give a coupling ratio between mitral cells consistent with experimental findings. Firing was induced with twenty current injections randomly located in the apical dendrite tuft of two of the mitral cells, mimicking the multiple inputs from the olfactory receptor neurons. A protocol was used to promote an initial asynchrony in firing which was transmitted across the gap-junctions to all six mitral cells. I found that the mitral cell population would overcome this asynchrony, rapidly tending to synchronous firing. Adding calcium and calcium dependent potassium channels to the mitral cells produced burst firing patterns that were different for each of the cells. The gap-junctions did not have enough influence to overcome the asynchrony of the different burst firing patterns. The addition of calcium concentration threshold dependant glutamate release and AMPA auto receptors to the apical dendrite tuft of each mitral cell allowed the burst firing to promote self propagating synchronised firing after an initial period of asynchrony