Sergio Solinas

A realistic large-scale model of the cerebellum granular layer predicts circuit spatio-temporal filtering properties

The way the cerebellar granular layer transforms incoming mossy fiber signals into new spike patterns to be related to Purkinje cells is not yet clear. Here, a realistic computational model of the granular layer was developed and used to address four main functional hypotheses: center-surround organization, time-windowing, high-pass filtering in responses to spike bursts and coherent oscillations in response to diffuse random activity. The model network was activated using patterns inspired by those recorded in vivo. Burst stimulation of a small mossy fiber bundle resulted in granule cell bursts delimited in time (time windowing) and space (center-surround) by network inhibition. This burst–burst transmission showed marked frequency-dependence configuring a high-pass filter with cut-off frequency around 100 Hz. The contrast between center and surround properties was regulated by the excitatory–inhibitory balance. The stronger excitation made the center more responsive to 10–50 Hz input frequencies and enhanced the granule cell output (with spikes occurring earlier and with higher frequency and number) compared to the surround. Finally, over a certain level of mossy fiber background activity, the circuit generated coherent oscillations in the theta-frequency band. All these processes were fine-tuned by NMDA and GABA-A receptor activation and neurotransmitter vesicle cycling in the cerebellar glomeruli. This model shows that available knowledge on cellular mechanisms is sufficient to unify the main functional hypotheses on the cerebellum granular layer and suggests that this network can behave as an adaptable spatio-temporal filter coordinated by theta-frequency oscillations.

Computational reconstruction of pacemaking and intrinsic electroresponsiveness in cerebellar golgi cells

The Golgi cells have been recently shown to beat regularly in vitro (Forti et al., 2006. J. Physiol. 574, 711–729). Four main currents were shown to be involved, namely a persistent sodium current (I Na-p), an h current (I h), an SK-type calcium-dependent potassium current (I K-AHP), and a slow M-like potassium current (I K-slow). These ionic currents could take part, together with others, also to different aspects of neuronal excitability like responses to depolarizing and hyperpolarizing current injection. However, the ionic mechanisms and their interactions remained largely hypothetical. In this work, we have investigated the mechanisms of Golgi cell excitability by developing a computational model. The model predicts that pacemaking is sustained by subthreshold oscillations tightly coupled to spikes. I Na-p and I K-slow emerged as the critical determinants of oscillations. I h also played a role by setting the oscillatory mechanism into the appropriate membrane potential range. I K-AHP, though taking part to the oscillation, appeared primarily involved in regulating the ISI following spikes. The combination with other currents, in particular a resurgent sodium current (I Na-r) and an A-current (I K-A), allowed a precise regulation of response frequency and delay. These results provide a coherent reconstruction of the ionic mechanisms determining Golgi cell intrinsic electroresponsiveness and suggests important implications for cerebellar signal processing, which will be fully developed in a companion paper (Solinas et al., 2008. Front. Neurosci. 2:4).

Fast-reset of pacemaking and theta-frequency resonance patterns in cerebellar golgi cells: simulations of their impact in vivo.

The Golgi cells are inhibitory interneurons of the cerebellar granular layer, which respond to afferent stimulation in vivo with a burst-pause sequence interrupting their irregular background low-frequency firing (Vos et al., 1999a. Eur. J. Neurosci. 11, 2621–2634). However, Golgi cells in vitro are regular pacemakers (Forti et al., 2006. J. Physiol. 574, 711–729), raising the question how their ionic mechanisms could impact on responses during physiological activity. Using patch-clamp recordings in cerebellar slices we show that the pacemaker cycle can be suddenly reset by spikes, making the cell highly sensitive to input variations. Moreover, the neuron resonates around the pacemaker frequency, making it specifically sensitive to patterned stimulation in the theta-frequency band. Computational analysis based on a model developed to reproduce Golgi cell pacemaking (Solinas et al., 2008 Front. Neurosci., 2:2) predicted that phase-reset required spike-triggered activation of SK channels and that resonance was sustained by a slow voltage-dependent potassium current and amplified by a persistent sodium current. Adding balanced synaptic noise to mimic the irregular discharge observed in vivo, we found that pacemaking converts into spontaneous irregular discharge, that phase-reset plays an important role in generating the burst-pause pattern evoked by sensory stimulation, and that repetitive stimulation at theta-frequency enhances the time-precision of spike coding in the burst. These results suggest that Golgi cell intrinsic properties exert a profound impact on time-dependent signal processing in the cerebellar granular layer.

The cerebellar network: From structure to function and dynamics

Since the discoveries of Camillo Golgi and Ramón y Cajal, the precise cellular organization of the cerebellum has inspired major computational theories, which have then influenced the scientific thought not only on the cerebellar function but also on the brain as a whole. However, six major issues revealing a discrepancy between morphologically inspired hypothesis and function have emerged. (1) The cerebellar granular layer does not simply operate a simple combinatorial decorrelation of the inputs but performs more complex non-linear spatio-temporal transformations and is endowed with synaptic plasticity. (2) Transmission along the ascending axon and parallel fibers does not lead to beam formation but rather to vertical columns of activation. (3) The olivo-cerebellar loop could perform complex timing operations rather than error detection and teaching. (4) Purkinje cell firing dynamics are much more complex than for a linear integrator and include pacemaking, burst-pause discharges, and bistable states in response to mossy and climbing fiber synaptic inputs. (5) Long-term synaptic plasticity is far more complex than traditional parallel fiber LTD and involves also other cerebellar synapses. (6) Oscillation and resonance could set up coherent cycles of activity designing a functional geometry that goes far beyond pre-wired anatomical circuits. These observations clearly show that structure is not sufficient to explain function and that a precise knowledge on dynamics is critical to understand how the cerebellar circuit operates.

Local Field Potential Modeling Predicts Dense Activation in Cerebellar Granule Cells Clusters under LTP and LTD Control

Local field-potentials (LFPs) are generated by neuronal ensembles and contain information about the activity of single neurons. Here, the LFPs of the cerebellar granular layer and their changes during long-term synaptic plasticity (LTP and LTD) were recorded in response to punctate facial stimulation in the rat in vivo. The LFP comprised a trigeminal (T) and a cortical (C) wave. T and C, which derived from independent granule cell clusters, co-varied during LTP and LTD. To extract information about the underlying cellular activities, the LFP was reconstructed using a repetitive convolution (ReConv) of the extracellular potential generated by a detailed multicompartmental model of the granule cell. The mossy fiber input patterns were determined using a Blind Source Separation (BSS) algorithm. The major component of the LFP was generated by the granule cell spike Na+ current, which caused a powerful sink in the axon initial segment with the source located in the soma and dendrites. Reproducing the LFP changes observed during LTP and LTD required modifications in both release probability and intrinsic excitability at the mossy fiber-granule cells relay. Synaptic plasticity and Golgi cell feed-forward inhibition proved critical for controlling the percentage of active granule cells, which was 11% in standard conditions but ranged from 3% during LTD to 21% during LTP and raised over 50% when inhibition was reduced. The emerging picture is that of independent (but neighboring) trigeminal and cortical channels, in which synaptic plasticity and feed-forward inhibition effectively regulate the number of discharging granule cells and emitted spikes generating “dense” activity clusters in the cerebellar granular layer.

Long-term inactivation particle for voltage-gated sodium channels.

Action potential generation is governed by the opening, inactivation, and recovery of voltage‐gated sodium channels. A channels voltage‐sensing and pore‐forming α subunit bears an intrinsic fast inactivation particle that mediates both onset of inactivation upon membrane depolarization and rapid recovery upon repolarization. We describe here a novel inactivation particle housed within an accessory channel subunit (A‐type FHF protein) that mediates rapid‐onset, long‐term inactivation of several sodium channels. The channel‐intrinsic and tethered FHF‐derived particles, both situated at the cytoplasmic face of the plasma membrane, compete for induction of inactivation, causing channels to progressively accumulate into the long‐term refractory state during multiple cycles of membrane depolarization. Intracellular injection of a short peptide corresponding to the FHF particle can reproduce channel long‐term inactivation in a dose‐dependent manner and can inhibit repetitive firing of cerebellar granule neurons. We discuss potential structural mechanisms of long‐term inactivation and potential roles of A‐type FHFs in the modulation of action potential generation and conduction.

The cerebellar Golgi cell and spatiotemporal organization of granular layer activity

The cerebellar granular layer has been suggested to perform a complex spatiotemporal reconfiguration of incoming mossy fiber signals. Central to this role is the inhibitory action exerted by Golgi cells over granule cells: Golgi cells inhibit granule cells through both feedforward and feedback inhibitory loops and generate a broad lateral inhibition that extends beyond the afferent synaptic field. This characteristic connectivity has recently been investigated in great detail and been correlated with specific functional properties of these neurons. These include theta-frequency pacemaking, network entrainment into coherent oscillations and phase resetting. Important advances have also been made in terms of determining the membrane and synaptic properties of the neuron, and clarifying the mechanisms of activation by input bursts. Moreover, voltage sensitive dye imaging and multi-electrode array (MEA) recordings, combined with mathematical simulations based on realistic computational models, have improved our understanding of the impact of Golgi cell activity on granular layer circuit computations. These investigations have highlighted the critical role of Golgi cells in: generating dense clusters of granule cell activity organized in center-surround structures, implementing combinatorial operations on multiple mossy fiber inputs, regulating transmission gain, and cut-off frequency, controlling spike timing and burst transmission, and determining the sign, intensity and duration of long-term synaptic plasticity at the mossy fiber-granule cell relay. This review considers recent advances in the field, highlighting the functional implications of Golgi cells for granular layer network computation and indicating new challenges for cerebellar research.

The Open Source Brain Initiative: enabling collaborative modelling in computational neuroscience

While an increasing number of biophysically detailed neuronal models (featuring (semi-) realistic morphologies and voltage and ligand gated conductances) are being shared across the community through resources like ModelDB, these usually only represent a snapshot of the model at the time of publication, in a format specific to the original simulator used. Models are constantly evolving however, to take account of new experimental findings and to address new research questions, both by the original modellers, and by other researchers who help provide quality control/debugging of original scripts and convert the model (components) for use in other simulators. This crucial part of the model life cycle is not well addressed with currently available infrastructure. The Open Source Brain (OSB) repository is being developed to provide a central location for researchers to collaboratively develop models which can be run across multiple simulators and can interact with the range of other applications in the NeuroML “ecosystem”. NeuroML [1] is a simulator independent language for expressing detailed single cell and network models, which is supported by an increasing number of applications for generating, visualising, simulating and analysing such models as well as by databases providing the base components (e.g. reconstructed morphologies, ion channels) for use in the models (http://www.neuroml. org/tool_support). The OSB repository differs from existing model databases which have traditionally concentrated on frozen, published models. The cell, ion channel, synapse and network models in this repository develop over time to ensure they reflect best practices in neurophysiological modelling and allow continuously improving, bug-free simulations. Multiple views of the model elements are available to encourage feedback from modellers, theoreticians and experimentalists. Links can be made to previous versions of the models in ModelDB, and deep links will be used to ensure cross referencing to other neuroinformatics resources such as NeuroMorpho and NeuroLex. The system is based around a Mercurial version control repository with models organised into projects illustrating a number of neurophysiologically relevant aspects of the cell and network behaviour. The history is recorded of all changes to each project by contributors who can be distributed worldwide. There is close integration with the application neuroConstruct [2], allowing the models to be examined with a 3D graphical user interface, and scripts automatically generated for use on a number of widely used neuronal simulators. A number of models are already available in the repository, including cell and network models from the cerebellum, detailed cortical and hippocampal pyramidal cell models and a 3D version of a single column thalamocortical network model [3]. While most of the models available are conversions of existing published models, some have been developed during original research projects using the tools and formats discussed here [4]. The repository is currently in alpha stage of development and is being tested with a small number of labs. The resource can be accessed at http://opensourcebrain.org:8080. This work has been primarily funded by the Wellcome Trust

Dendritic amplification of inhibitory postsynaptic potentials in a model Purkinje cell

In neurons with large dendritic arbors, the postsynaptic potentials interact in a complex manner with active and passive membrane properties, causing not easily predictable transformations during the propagation from synapse to soma. Previous theoretical and experimental studies in both cerebellar Purkinje cells and neocortical pyramidal neurons have shown that voltage‐dependent ion channels change the amplitude and time‐course of postsynaptic potentials. We investigated the mechanisms involved in the propagation of inhibitory postsynaptic potentials (IPSPs) along active dendrites in a model of the Purkinje cell. The amplitude and time‐course of IPSPs recorded at the soma were dependent on the synaptic distance from the soma, as predicted by passive cable theory. We show that the effect of distance on the amplitude and width of the IPSP was significantly reduced by the dendritic ion channels, whereas the rise time was not affected. Somatic IPSPs evoked by the activation of the most distal synapses were up to six times amplified owing to the presence of voltage‐gated channels and the IPSP width became independent of the covered distance. A transient deactivation of the Ca2+ channels and the Ca2+‐dependent K+ channels, triggered by the hyperpolarization following activation of the inhibitory synapse, was found to be responsible for these dynamics. Nevertheless, the position of activated synapses had a marked effect on the Purkinje cell firing pattern, making stellate cells and basket cells most suitable for controlling the firing rate and spike timing, respectively, of their target Purkinje cells.

Theta-Frequency Resonance at the Cerebellum Input Stage Improves Spike Timing on the Millisecond Time-Scale

The neuronal circuits of the brain are thought to use resonance and oscillations to improve communication over specific frequency bands (Llinas, 1988; Buzsaki, 2006). However, the properties and mechanism of these phenomena in brain circuits remain largely unknown. Here we show that, at the cerebellum input stage, the granular layer (GRL) generates its maximum response at 5–7 Hz both in vivo following tactile sensory stimulation of the whisker pad and in acute slices following mossy fiber bundle stimulation. The spatial analysis of GRL activity performed using voltage-sensitive dye (VSD) imaging revealed 5–7 Hz resonance covering large GRL areas. In single granule cells, resonance appeared as a reorganization of output spike bursts on the millisecond time-scale, such that the first spike occurred earlier and with higher temporal precision and the probability of spike generation increased. Resonance was independent from circuit inhibition, as it persisted with little variation in the presence of the GABAA receptor blocker, gabazine. However, circuit inhibition reduced the resonance area more markedly at 7 Hz. Simulations with detailed computational models suggested that resonance depended on intrinsic granule cells ionic mechanisms: specifically, Kslow (M-like) and KA currents acted as resonators and the persistent Na current and NMDA current acted as amplifiers. This form of resonance may play an important role for enhancing coherent spike emission from the GRL when theta-frequency bursts are transmitted by the cerebral cortex and peripheral sensory structures during sensory-motor processing, cognition, and learning.