Gap junctions synchronize synaptic input rather than spike output of olivary neurons

Electronic coupling in the inferior olive is supposed to underlie the synchrony of complex spike activities of Purkinje cells in the cerebellar cortex. Here we show a computational model which suggests that the olivary gap junctions may synchronize the input rather than the neuronal output. As such, coupling may influence the absolute moment in time of the complex spike activity rather than their synchrony.

Analysis of Cx36 knockout does not support tenet that olivary gap junctions are required for complex spike synchronization and normal motor performance

Electrotonic coupling by gap junctions between neurons in the inferior olive has been claimed to underly complex spike (CS) synchrony of Purkinje cells in the cerebellar cortex and thereby to play a role in the coordination of movements. Here, we investigated the motor performance of mice that lack connexin36 (Cx36), which appears necessary for functional olivary gap junctions. Cx36 null-mutants are not ataxic, they show a normal performance on the accelerating rotorod, and they have a regular walking pattern. In addition, they show normal compensatory eye movements during sinusoidal visual and/or vestibular stimulation. To find out whether the normal motor performance in mutants reflects normal CS activity or some compensatory mechanism downstream of the cerebellar cortex, we determined the CS firing rate, climbing-fiber pause, and degree of CS synchrony. None of these parameters in the mutants differed from those in wildtype littermates. Finally, we investigated whether the role of coupling becomes apparent under challenging conditions, such as during application of the tremorgenic drug harmaline, which specifically turns olivary neurons into an oscillatory state at a high frequency. In both the mutants and wildtypes this application induced tremors of a similar duration with similar peak frequencies and amplitudes. Thus surprisingly, the present data does not support the notion that electrotonic coupling by gap junctions underlies synchronization of olivary spike activity and that these gap junctions are essential for normal motor performance.

Stability properties of solitary waves and periodic wave trains in a two-dimensional network of spiking neurons

We investigate solitary waves of excitation in a two-dimensional network of spiking neurons with distance-dependent couplings. A continuum description is developed that does not require spatial or temporal averaging. Using this description, propagation velocities and dispersion relations for solitary waves and periodic wave trains can be calculated analytically. We show that the stability properties of solitary waves and wave trains are dominated by form instabilities which are genuine to the two-dimensional nature of the system.

Time window control: a model for cerebellar function based on synchronization, reverberation, and time slicing

We present a new hypothesis of cerebellar function that is based on synchronization, delayed reverberation, and time windows for triggering spikes. Our model suggests that granule cells admit mossy fiber activity to the parallel fibers only if the Golgi cells are firing synchronously and if the mossy-fiber spikes arrive within short and well-defined time windows. The concept of time window control organizes neuronal activity in discrete 'time slices' that can be used to discern meaningful information from background noise. In particular, Purkinje cell activity can trigger rebound spikes in deep cerebellar nuclei cells, which project via brain stem nuclei and mossy fibers back to the cerebellar cortex. Using a detailed model of deep cerebellar nuclei cells, we demonstrate that the delayed firing of rebound spikes is a robust mechanism so as to ensure that the reverberated activity re-arrives in the mossy fibers just during the granule-cell time window. Large network simulations reveal that synaptic plasticity (LTD and LTP) at the parallel fiber/Purkinje cell synapses that relies on the timing of the parallel fiber and climbing fiber activities allows the system to learn, store, and recall spatiotemporal patterns of spike activity. Climbing fiber spikes function both as teacher and as synchronization signals. The temporal characteristics of the climbing fiber activity are due to intrinsic oscillatory properties of inferior olivary neurons and to reverberating projections between deep cerebellar nuclei, the mesodiencephalic junction, and the inferior olive. Thus, the reverberating loops of the mossy fiber system and climbing fiber system may interact directly with the time windows provided by the circuitry of the cerebellar cortex so as to generate the appropriate spatio-temporal firing patterns in the deep cerebellar nuclei neurons that control premotor systems. In future studies the model will be extended in that high frequency simple spike activities will be included and that their relevance for motor control will be addressed.

Modeling synaptic plasticity in conjuction with the timing of pre- and postsynaptic action potentials

We present a spiking neuron model that allows for an analytic calculation of the correlations between pre- and postsynaptic spikes. The neuron model is a generalization of the integrate-and-fire model and equipped with a probabilistic spike-triggering mechanism. We show that under certain biologically plausible conditions, pre- and postsynaptic spike trains can be described simultaneously as an inhomogeneous Poisson process. Inspired by experimental findings, we develop a model for synaptic long-term plasticity that relies on the relative timing of pre- and post-synaptic action potentials. Being given an input statistics, we compute the stationary synaptic weights that result from the temporal correlations between the pre- and postsynaptic spikes. By means of both analytic calculations and computer simulations, we show that such a mechanism of synaptic plasticity is able to strengthen those input synapses that convey precisely timed spikes at the expense of synapses that deliver spikes with a broad temporal distribution. This may be of vital importance for any kind of information processing based on spiking neurons and temporal coding.

Delayed reverberation through time windows as a key to cerebellar function

We present a functional model of the cerebellum comprising cerebellar cortex, inferior olive, deep cerebellar nuclei, and brain stem nuclei. The discerning feature of the model being time coding, we consistently describe the system in terms of postsynaptic potentials, synchronous action potentials, and propagation delays. We show by means of detailed single-neuron modeling that (i) Golgi cells can fulfill a gating task in that they form short and well-defined time windows within which granule cells can reach firing threshold, thus organizing neuronal activity in discrete 'time slices', and that (ii) rebound firing in cerebellar nuclei cells is a robust mechanism leading to a delayed reverberation of Purkinje cell activity through cerebellar-reticular projections back to the cerebellar cortex. Computer simulations of the whole cerebellar network consisting of several thousand neurons reveal that reverberation in conjunction with long-term plasticity at the parallel fiber-Purkinje cell synapses enables the system to learn, store, and recall spatio-temporal patterns of neuronal activity. Climbing fiber spikes act both as a synchronization and as a teacher signal, not as an error signal. They are due to intrinsic oscillatory properties of inferior olivary neurons and to delayed reverberation within the network. In addition to clear experimental predictions the present theory sheds new light on a number of experimental observation such as the synchronicity of climbing fiber spikes and provides a novel explanation of how the cerebellum solves timing tasks on a time scale of several hundreds of milliseconds.

Short-term synaptic plasticity and network behavior

We develop a minimal time-continuous model for use-dependent synaptic short-term plasticity that can account for both short-term depression and short-term facilitation. It is analyzed in the context of the spike response neuron model. Explicit expressions are derived for the synaptic strength as a function of previous spike arrival times. These results are then used to investigate the behavior of large networks of highly interconnected neurons in the presence of short-term synaptic plasticity. We extend previous results so as to elucidate the existence and stability of limit cycles with coherently firing neurons. After the onset of an external stimulus, we have found complex transient network behavior that manifests itself as a sequence of different modes of coherent firing until a stable limit cycle is reached.