Predicting spike timing of neocortical pyramidal neurons by simple threshold models

Neurons generate spikes reliably with millisecond precision if driven by a fluctuating current--is it then possible to predict the spike timing knowing the input? We determined parameters of an adapting threshold model using data recorded in vitro from 24 layer 5 pyramidal neurons from rat somatosensory cortex, stimulated intracellularly by a fluctuating current simulating synaptic bombardment in vivo. The model generates output spikes whenever the membrane voltage (a filtered version of the input current) reaches a dynamic threshold. We find that for input currents with large fluctuation amplitude, up to 75% of the spike times can be predicted with a precision of +/-2 ms. Some of the intrinsic neuronal unreliability can be accounted for by a noisy threshold mechanism. Our results suggest that, under random current injection into the soma, (i) neuronal behavior in the subthreshold regime can be well approximated by a simple linear filter; and (ii) most of the nonlinearities are captured by a simple threshold process.

Spine Ca2+ signaling in spike-timing-dependent plasticity

Calcium is a second messenger, which can trigger the modification of synaptic efficacy. We investigated the question of whether a differential rise in postsynaptic Ca2+ ([Ca2+]i) alone is sufficient to account for the induction of long-term potentiation (LTP) and long-term depression (LTD) of EPSPs in the basal dendrites of layer 2/3 pyramidal neurons of the somatosensory cortex. Volume-averaged [Ca2+]i transients were measured in spines of the basal dendritic arbor for spike-timing-dependent plasticity induction protocols. The rise in [Ca2+]i was uncorrelated to the direction of the change in synaptic efficacy, because several pairing protocols evoked similar spine [Ca2+]i transients but resulted in either LTP or LTD. The sequence dependence of near-coincident presynaptic and postsynaptic activity on the direction of changes in synaptic strength suggested that LTP and LTD were induced by two processes, which were controlled separately by postsynaptic [Ca2+]i levels. Activation of voltage-dependent Ca2+ channels before metabotropic glutamate receptors (mGluRs) resulted in the phospholipase C-dependent (PLC-dependent) synthesis of endocannabinoids, which acted as a retrograde messenger to induce LTD. LTP required a large [Ca2+]i transient evoked by NMDA receptor activation. Blocking mGluRs abolished the induction of LTD and uncovered the Ca2+-dependent induction of LTP. We conclude that the volume-averaged peak elevation of [Ca2+]i in spines of layer 2/3 pyramids determines the magnitude of long-term changes in synaptic efficacy. The direction of the change is controlled, however, via a mGluR-coupled signaling cascade. mGluRs act in conjunction with PLC as sequence-sensitive coincidence detectors when postsynaptic precede presynaptic action potentials to induce LTD. Thus presumably two different Ca2+ sensors in spines control the induction of spike-timing-dependent synaptic plasticity.

Eluding oblivion with smart stochastic selection of synaptic updates

The variables involved in the equations that describe realistic synaptic dynamics always vary in a limited range. Their boundedness makes the synapses forgetful, not for the mere passage of time, but because new experiences overwrite old memories. The forgetting rate depends on how many synapses are modified by each new experience: many changes means fast learning and fast forgetting, whereas few changes means slow learning and long memory retention. Reducing the average number of modified synapses can extend the memory span at the price of a reduced amount of information stored when a new experience is memorized. Every trick which allows to slow down the learning process in a smart way can improve the memory performance. We review some of the tricks that allow to elude fast forgetting (oblivion). They are based on the stochastic selection of the synapses whose modifications are actually consolidated following each new experience. In practice only a randomly selected, small fraction of the synapses eligible for an update are actually modified. This allows to acquire the amount of information necessary to retrieve the memory without compromising the retention of old experiences. The fraction of modified synapses can be further reduced in a smart way by changing synapses only when it is really necessary, i.e. when the post-synaptic neuron does not respond as desired. Finally we show that such a stochastic selection emerges naturally from spike driven synaptic dynamics which read noisy pre and post-synaptic neural activities. These activities can actually be generated by a chaotic system.

Learning real-world stimuli in a neural network with spike-driven synaptic dynamics

We present a model of spike-driven synaptic plasticity inspired by experimental observations and motivated by the desire to build an electronic hardware device that can learn to classify complex stimuli in a semisupervised fashion. During training, patterns of activity are sequentially imposed on the input neurons, and an additional instructor signal drives the output neurons toward the desired activity. The network is made of integrate-and-fire neurons with constant leak and a floor. The synapses are bistable, and they are modified by the arrival of presynaptic spikes. The sign of the change is determined by both the depolarization and the state of a variable that integrates the postsynaptic action potentials. Following the training phase, the instructor signal is removed, and the output neurons are driven purely by the activity of the input neurons weighted by the plastic synapses. In the absence of stimulation, the synapses preserve their internal state indefinitely. Memories are also very robust to the disruptive action of spontaneous activity. A network of 2000 input neurons is shown to be able to classify correctly a large number (thousands) of highly overlapping patterns (300 classes of preprocessed Latex characters, 30 patterns per class, and a subset of the NIST characters data set) and to generalize with performances that are better than or comparable to those of artificial neural networks. Finally we show that the synaptic dynamics is compatible with many of the experimental observations on the induction of long-term modifications (spike-timing-dependent plasticity and its dependence on both the postsynaptic depolarization and the frequency of pre- and postsynaptic neurons).

Spindle burst like spike discharge oscillations in organotypic cultures of neonatal rat cortex

Early network oscillations and spindle bursts are typical patterns of spontaneous rhythmic activity in cortical networks of neonatal rodents in vivo and in vitro. The latter can also be triggered in vivo by stimulation of afferent inputs. The mechanisms underlying such oscillations undergo profound developmental changes in the first postnatal weeks. Their possible role in cortical development is postulated but not known in detail. We have studied spontaneous and evoked patterns of activity in organotypic cultures of slices from neonatal rat cortex grown on multielectrode arrays (MEAs) for extracellular single- and multi-unit recording. Episodes of spontaneous spike discharge oscillations at 7 - 25 Hz lasting for 0.6 - 3 seconds appeared in about half of these cultures spontaneously and could be triggered by electrical stimulation of few distinct electrodes. These oscillations usually covered only restricted areas of the slices. Besides oscillations, single population bursts that spread in a wavelike manner over the whole slice also appeared spontaneously and were triggered by electrical stimulation. In most but not all cultures, population bursts preceded the oscillations. Both population bursts and spike discharge oscillations required intact glutamatergic synaptic transmission since they were suppressed by the AMPA/kainate glutamate receptor antagonist CNQX. The NMDA antagonist d-APV suppressed the oscillations but not the population bursts, suggesting an involvement of NMDA receptors in the oscillations. These findings show that spindle burst like cortical rhythms are reproduced in organotypic cultures of neonatal cortex. The culture model thus allows investigating the role of such rhythms in cortical circuit formation. Supported by SNF grant No. 3100A0-107641/1.