Modeling of spontaneous activity in developing spinal cord using activity-dependent depression in an excitatory network.

Spontaneous episodic activity is a general feature of developing neural networks. In the chick spinal cord, the activity comprises episodes of rhythmic discharge (duration 5-90 sec; cycle rate 0.1-2 Hz) that recur every 2-30 min. The activity does not depend on specialized connectivity or intrinsic bursting neurons and is generated by a network of functionally excitatory connections. Here, we develop an idealized, qualitative model of a homogeneous, excitatory recurrent network that could account for the multiple time-scale spontaneous activity in the embryonic chick spinal cord. We show that cycling can arise from the interplay between excitatory connectivity and fast synaptic depression. The slow episodic behavior is attributable to a slow activity-dependent network depression that is modeled either as a modulation of cellular excitability or as synaptic depression. Although the two descriptions share many features, the model with a slow synaptic depression accounts better for the experimental observations during blockade of excitatory synapses.

An algorithm for modifying neurotransmitter release probability based on pre- and postsynaptic spike timing.

The precise times of occurrence of individual pre- and postsynaptic action potentials are known to play a key role in the modification of synaptic efficacy. Based on stimulation protocols of two synaptically connected neurons, we infer an algorithm that reproduces the experimental data by modifying the probability of vesicle discharge as a function of the relative timing of spikes in the pre- and postsynaptic neurons. The primary feature of this algorithm is an asymmetry with respect to the direction of synaptic modification depending on whether the presynaptic spikes precede or follow the postsynaptic spike. Specifically, if the presynaptic spike occurs up to 50 ms before the postsynaptic spike, the probability of vesicle discharge is upregulated, while the probability of vesicle discharge is downregulated if the presynaptic spike occurs up to 50 ms after the postsynaptic spike. When neurons fire irregularly with Poisson spike trains at constant mean firing rates, the probability of vesicle discharge converges toward a characteristic value determined by the pre- and postsynaptic firing rates. On the other hand, if the mean rates of the Poisson spike trains slowly change with time, our algorithm predicts modifications in the probability of release that generalize Hebbian and Bienenstock-Cooper-Munro rules. We conclude that the proposed spike-based synaptic learning algorithm provides a general framework for regulating neurotransmitter release probability.

Spike-based synaptic plasticity and the emergence of direction selective simple cells: mathematical analysis.

In the companion paper we presented extended simulations showing that the recently observed spike-timing dependent synaptic plasticity can explain the development of simple cell direction selectivity (DS) when simultaneously modifying the synaptic strength and the degree of synaptic depression. Here we estimate the spatial shift of the simple cell receptive field (RF) induced by the long-term synaptic plasticity, and the temporal phase advance caused by the short-term synaptic depression in response to drifting grating stimuli. The analytical expressions for this spatial shift and temporal phase advance lead to a qualitative reproduction of the frequency tuning curves of non-directional and directional simple cells. In agreement with in vivo recordings, the acquired DS is strongest for test gratings with a temporal frequency around 1-4 Hz. In our model this best frequency is determined by the width of the learning function and the time course of depression, but not by the temporal frequency of the 'training' stimuli. The analysis further reveals the instability of the initially symmetric RF, and formally explains why direction selectivity develops from a non-directional cell in a natural, directionally unbiased stimulation scenario.

Reading neuronal synchrony with depressing synapses.

A recent experiment showed that neurons in the primary auditory cortex of the monkey do not change their mean firing rate during an ongoing tone stimulus. The only change was an enhanced correlation among the individual spike trains during the tone. We show that there is an easy way to extract this coherence information in the cortical cell population by projecting the spike trains through depressing synapses onto a postsynaptic neuron.

Spike-based synaptic plasticity and the emergence of direction selective simple cells: simulation results.

Direction selectivity (DS) of simple cells in the primary visual cortex was recently suggested to arise from short-term synaptic depression in thalamocortical afferents (Chance F, Nelson S, Abbott L (1998), J. Neuroscience 18(12): 4785-4799). In the model, two groups of afferents with spatially displaced receptive fields project through either depressing and non-depressing synapses onto the V1 cell. The degree of synaptic depression determines the temporal phase advance of the response to drifting gratings. We show that the spatial displacement and the appropriate degree of synaptic depression required for DS can develop within an unbiased input scenario by means of temporally asymmetric spike-timing dependent plasticity (STDP) which modifies both the synaptic strength and the degree of synaptic depression. Moving stimuli of random velocities and directions break any initial receptive field symmetry and produce DS. Frequency tuning curves and subthreshold membrane potentials akin to those measured for non-directional simple cells are thereby changed into those measured for directional cells. If STDP is such that down-regulation dominates up-regulation the overall synaptic strength adapts in a self-organizing way such that eventually the postsynaptic response for the non-preferred direction becomes subthreshold. To prevent unlearning of the acquired DS by randomly changing stimulus directions an additional learning threshold is necessary. To further protect the development of the simple cell properties against noise in the stimulus, asynchronous and irregular synaptic inputs are required.

Size principle and information theory.

The motor units of a skeletal muscle may be recruited according to different strategies. From all possible recruitment strategies nature selected the simplest one: in most actions of vertebrate skeletal muscles the recruitment of its motor units is by increasing size. This so-called size principle permits a high precision in muscle force generation since small muscle forces are produced exclusively by small motor units. Larger motor units are activated only if the total muscle force has already reached certain critical levels. We show that this recruitment by size is not only optimal in precision but also optimal in an information theoretical sense. We consider the motoneuron pool as an encoder generating a parallel binary code from a common input to that pool. The generated motoneuron code is sent down through the motoneuron axons to the muscle. We establish that an optimization of this motoneuron code with respect to its information content is equivalent to the recruitment of motor units by size. Moreover, maximal information content of the motoneuron code is equivalent to a minimal expected error in muscle force generation.

Transmitter concentration profiles in the synaptic cleft: an analytical model of release and diffusion.

A three-dimensional model for release and diffusion of glutamate in the synaptic cleft was developed and solved analytically. The model consists of a source function describing transmitter release from the vesicle and a diffusion function describing the spread of transmitter in the cleft. Concentration profiles of transmitter at the postsynaptic side were calculated for different transmitter concentrations in a vesicle, release scenarios, and diffusion coefficients. From the concentration profiles the receptor occupancy could be determined using alpha-amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid receptor kinetics. It turned out that saturation of receptors and sufficiently fast currents could only be obtained if the diffusion coefficient was one order of magnitude lower than generally assumed, and if the postsynaptic receptors formed clusters with a diameter of roughly 100 nm directly opposite the release sites. Under these circumstances the gradient of the transmitter concentration at the postsynaptic membrane outside the receptor clusters was steep, with minimal cross-talk among neighboring receptor clusters. These findings suggest that for each release site a corresponding receptor aggregate exists, subdividing an individual synapse into independent functional subunits without the need for specific lateral diffusion barriers.

Pattern generation by two coupled time-discrete neural networks with synaptic depression.

Numerous animal behaviors, such as locomotion in vertebrates, are produced by rhythmic contractions that alternate between two muscle groups. The neuronal networks generating such alternate rhythmic activity are generally thought to rely on pacemaker cells or well-designed circuits consisting of inhibitory and excitatory neurons. However, experiments in organotypic cultures of embryonic rat spinal cord have shown that neuronal networks with purely excitatory and random connections may oscillate due to their synaptic depression, even without pacemaker cells. In this theoretical study, we investigate what happens if two such networks are symmetrically coupled by a small number of excitatory connections. We discuss a time-discrete mean-field model describing the average activity and the average synaptic depression of the two networks. Depending on the parameter values of the depression, the oscillations will be in phase, antiphase, quasiperiodic, or phase trapped. We put forward the hypothesis that pattern generators may rely on activity-dependent tuning of synaptic depression.