Computational Properties of Cerebellar Nucleus Neurons: Effects of Stochastic Ion Channel Gating and Input Location

The function of the nervous system is shaped by the refined integration of synaptic inputs taking place at the single neuron level. Gain modulation is a computational principle that is widely used across the brain, in which the response of a neuronal unit to a set of inputs is affected in a multiplicative fashion by a second set of inputs, but without any effect on its selectivity. The arithmetic operations performed by pyramidal cells in cortical brain areas have been well characterised, along with the underlying mechanisms at the level of networks and cells, for instance background synaptic noise and dendritic saturation. However, in spite of the vast amount of research on the cerebellum and its function, little is known about neuronal computations carried out by its cellular components. A particular area of interest are the cerebellar nuclei, the main output gate of the cerebellum to the brain stem and cortical areas. The aim of this thesis is to contribute to an understanding of the arithmetic operations performed by neurons in the cerebellar nuclei. Focus is placed on two putative determinants, the location of the synaptic input and the presence of channel noise. To analyse the effect of channel noise, the known voltage-gated ion channels of a cerebellar nucleus neuron model are translated to stochastic Markov formalisms and their electrophysiologial behaviour is compared to their deterministic Hodgkin-Huxley counterparts. The findings demonstrate that in most cases, the behaviour of stochastic channels matches the reference deterministic models, with the notable exception of voltage-gated channels with fast kinetics. Two potential explanations are suggested for this discrepancy. Firstly, channels with fast kinetics are strongly affected by the artefactual loss of gating events in the simulation that is caused by the use of a finite-length time step. While this effect can be mitigated, in part, by using very small time steps, the second source of simulation artefacts is the rectification of the distribution of open channels, when channel kinetics characteristics allow the generation of a window current, with an temporal-averaged equilibrium close to zero. Further, stochastic gating is implemented in a realistic cerebellar nucleus neuronal model. The resulting stochastic model exhibits probabilistic spiking and a similar output rate as the corresponding deterministic cerebellar nucleus neuronal model. However, the outcomes of this thesis indicate the computational properties of the cerebellar nucleus neuronal model are independent of the presence of ion channel noise. The main result of this thesis is that the synaptic input location determines the single neuron computational properties, both in the cerebellar nucleus and layer Vb pyramidal neuronal models. The extent of multiplication increases systematically with the distance from the soma, for the cerebellar nucleus, but not for the layer Vb pyramidal neuron, where it is smaller than it would be expected for the distance from the soma. For both neurons, the underlying mechanism is related to the combined effect of nonlinearities introduced by dendritic saturation and the synaptic input noise. However, while excitatory inputs in the perisomatic areas in the cerebellar nucleus undergo additive operations and the distal areas multiplicative, in the layer Vb pyramidal neuron the integration of the excitatory driving input is always multiplicative. In addition, the change in gain is sensitive to the synchronicity of the excitatory synaptic input in the layer Vb pyramidal neuron, but not in the cerebellar nucleus neuron. These observations indicate that the same gain control mechanism might be utilized in distinct ways, in different computational contexts and across different areas, based on the neuronal type and its function

Frontiers of Membrane Computing: Open Problems and Research Topics

This is a list of open problems and research topics collected after the Twelfth Conference on Membrane Computing, CMC 2012 (Fontainebleau, France (23 - 26 August 2011), meant initially to be a working material for Tenth Brainstorming Week on Membrane Computing, Sevilla, Spain (January 30 - February 3, 2012). The result was circulated in several versions before the brainstorming and then modified according to the discussions held in Sevilla and according to the progresses made during the meeting. In the present form, the list gives an image about key research directions currently active in membrane computing

Automated optimization of a reduced layer 5 pyramidal cell model based on experimental data.

The construction of compartmental models of neurons involves tuning a set of parameters to make the model neuron behave as realistically as possible. While the parameter space of single-compartment models or other simple models can be exhaustively searched, the introduction of dendritic geometry causes the number of parameters to balloon. As parameter tuning is a daunting and time-consuming task when performed manually, reliable methods for automatically optimizing compartmental models are desperately needed, as only optimized models can capture the behavior of real neurons. Here we present a three-step strategy to automatically build reduced models of layer 5 pyramidal neurons that closely reproduce experimental data. First, we reduce the pattern of dendritic branches of a detailed model to a set of equivalent primary dendrites. Second, the ion channel densities are estimated using a multi-objective optimization strategy to fit the voltage trace recorded under two conditions - with and without the apical dendrite occluded by pinching. Finally, we tune dendritic calcium channel parameters to model the initiation of dendritic calcium spikes and the coupling between soma and dendrite. More generally, this new method can be applied to construct families of models of different neuron types, with applications ranging from the study of information processing in single neurons to realistic simulations of large-scale network dynamics

Stochastic Ion Channel Gating in Dendritic Neurons: Morphology Dependence and Probabilistic Synaptic Activation of Dendritic Spikes

Neuronal activity is mediated through changes in the probability of stochastic transitions between open and closed states of ion channels. While differences in morphology define neuronal cell types and may underlie neurological disorders, very little is known about influences of stochastic ion channel gating in neurons with complex morphology. We introduce and validate new computational tools that enable efficient generation and simulation of models containing stochastic ion channels distributed across dendritic and axonal membranes. Comparison of five morphologically distinct neuronal cell types reveals that when all simulated neurons contain identical densities of stochastic ion channels, the amplitude of stochastic membrane potential fluctuations differs between cell types and depends on sub-cellular location. For typical neurons, the amplitude of membrane potential fluctuations depends on channel kinetics as well as open probability. Using a detailed model of a hippocampal CA1 pyramidal neuron, we show that when intrinsic ion channels gate stochastically, the probability of initiation of dendritic or somatic spikes by dendritic synaptic input varies continuously between zero and one, whereas when ion channels gate deterministically, the probability is either zero or one. At physiological firing rates, stochastic gating of dendritic ion channels almost completely accounts for probabilistic somatic and dendritic spikes generated by the fully stochastic model. These results suggest that the consequences of stochastic ion channel gating differ globally between neuronal cell-types and locally between neuronal compartments. Whereas dendritic neurons are often assumed to behave deterministically, our simulations suggest that a direct consequence of stochastic gating of intrinsic ion channels is that spike output may instead be a probabilistic function of patterns of synaptic input to dendrites

Data-driven reduction of dendritic morphologies with preserved dendro-somatic responses

Dendrites shape information flow in neurons. Yet, there is little consensus on the level of spatial complexity at which they operate. Through carefully chosen parameter fits, solvable in the least-squares sense, we obtain accurate reduced compartmental models at any level of complexity. We show that (back-propagating) action potentials, Ca2+ spikes, and N-methyl-D-aspartate spikes can all be reproduced with few compartments. We also investigate whether afferent spatial connectivity motifs admit simplification by ablating targeted branches and grouping affected synapses onto the next proximal dendrite. We find that voltage in the remaining branches is reproduced if temporal conductance fluctuations stay below a limit that depends on the average difference in input resistance between the ablated branches and the next proximal dendrite. Furthermore, our methodology fits reduced models directly from experimental data, without requiring morphological reconstructions. We provide software that automatizes the simplification, eliminating a common hurdle toward including dendritic computations in network models

Symposium on Frontiers of Molecular Neurobiology

Membrane structure, synaptic transmission, and fibrous proteins of neurons - conferenc

Neuromodulation impact on nonlinear firing behavior of a reduced model motoneuron with the active dendrite

Neuromodulatory inputs from brainstem systems modulate the normal function of spinal motoneurons by altering the activation properties of persistent inward currents (PICs) in their dendrites. However, the effect of the PIC on firing outputs also depends on its location in the dendritic tree. To investigate the interaction between PIC neuromodulation and PIC location dependence, we used a two-compartment model that was biologically realistic in that it retains directional and frequency-dependent electrical coupling between the soma and the dendrites, as seen in multi-compartment models based on full anatomical reconstructions of motoneurons. Our two-compartment approach allowed us to systematically vary the coupling parameters between the soma and the dendrite to accurately reproduce the effect of location of the dendritic PIC on the generation of nonlinear (hysteretic) motoneuron firing patterns. Our results show that as a single parameter value for PIC activation was either increased or decreased by 20% from its default value, the solution space of the coupling parameter values for nonlinear firing outputs was drastically reduced by approximately 80%. As a result, the model tended to fire only in a linear mode at the majority of dendritic PIC sites. The same results were obtained when all parameters for the PIC activation simultaneously changed only by approximately ±10%. Our results suggest the democratization effect of neuromodulation: the neuromodulation by the brainstem systems may play a role in switching the motoneurons with PICs at different dendritic locations to a similar mode of firing by reducing the effect of the dendritic location of PICs on the firing behavior