Astrocytes have been shown to modulate synaptic transmission and plasticity in specific cortical synapses, but our understanding of the underlying molecular and cellular mechanisms remains limited. Here we present a new biophysicochemical model of a somatosensory cortical layer 4 to layer 2/3 synapse to study the role of astrocytes in spike-timing-dependent long-term depression (t-LTD) in vivo. By applying the synapse model and electrophysiological data recorded from rodent somatosensory cortex, we show that a signal from a postsynaptic neuron, orchestrated by endocannabinoids, astrocytic calcium signaling, and presynaptic N-methyl-D-aspartate receptors coupled with calcineurin signaling, induces t-LTD which is sensitive to the temporal difference between post- and presynaptic firing. We predict for the first time the dynamics of astrocyte-mediated molecular mechanisms underlying t-LTD and link complex biochemical networks at presynaptic, postsynaptic, and astrocytic sites to the time window of t-LTD induction. During t-LTD a single astrocyte acts as a delay factor for fast neuronal activity and integrates fast neuronal sensory processing with slow non-neuronal processing to modulate synaptic properties in the brain. Our results suggest that astrocytes play a critical role in synaptic computation during postnatal development and are of paramount importance in guiding the development of brain circuit functions, learning and memory.

We use a computational model of a hippocampal CA1 pyramidal cell to demonstrate that spine head calcium provides an instantaneous readout at each synapse of the postsynaptic weighted sum of all presynaptic activity impinging on the cell. The form of the readout is equivalent to the functions of weighted, summed inputs used in neural network learning rules. Within a dendritic layer, peak spine head calcium levels are either a linear or sigmoidal function of the number of coactive synapses, with nonlinearity depending on the ability of voltage spread in the dendrites to reach calcium spike threshold. This is strongly controlled by the potassium A-type current, with calcium spikes and the consequent sigmoidal increase in peak spine head calcium present only when the A-channel density is low. Other membrane characteristics influence the gain of the relationship between peak calcium and the number of active synapses. In particular, increasing spine neck resistance increases the gain due to increased voltage responses to synaptic input in spine heads. Colocation of stimulated synapses on a single dendritic branch also increases the gain of the response. Input pathways cooperate: CA3 inputs to the proximal apical dendrites can strongly amplify peak calcium levels due to weak EC input to the distal dendrites, but not so strongly vice versa. CA3 inputs to the basal dendrites can boost calcium levels in the proximal apical dendrites, but the relative electrical compactness of the basal dendrites results in the reverse effect being less significant. These results give pointers as to how to better describe the contributions of pre- and postsynaptic activity in the learning "rules" that apply in these cells. The calcium signal is closer in form to the activity measures used in traditional neural network learning rules than to the spike times used in spike-timing-dependent plasticity.

Spike-timing-dependent plasticity (STDP) is described by long-term potentiation (LTP), when a presynaptic event precedes a postsynaptic event, and by long-term depression (LTD), when the temporal order is reversed. In this article, we present a biophysical model of STDP based on a differential Hebbian learning rule (ISO learning). This rule correlates presynaptically the NMDA channel conductance with the derivative of the membrane potential at the synapse as the postsynaptic signal. The model is able to reproduce the generic STDP weight change characteristic. We find that (1) The actual shape of the weight change curve strongly depends on the NMDA channel characteristics and on the shape of the membrane potential at the synapse. (2) The typical antisymmetrical STDP curve (LTD and LTP) can become similar to a standard Hebbian characteristic (LTP only) without having to change the learning rule. This occurs if the membrane depolarization has a shallow onset and is long lasting. (3) It is known that the membrane potential varies along the dendrite as a result of the active or passive backpropagation of somatic spikes or because of local dendritic processes. As a consequence, our model predicts that learning properties will be different at different locations on the dendritic tree. In conclusion, such site-specific synaptic plasticity would provide a neuron with powerful learning capabilities.

Spike timing plasticity (STDP) is a special form of synaptic plasticity where the relative timing of post- and presynaptic activity determines the change of the synaptic weight. On the postsynaptic side, active back- propagating spikes in dendrites seem to play a crucial role in the induc- tion of spike timing dependent plasticity. We argue that postsynaptically the temporal change of the membrane potential determines the weight change. Coming from the presynaptic side induction of STDP is closely related to the activation of NMDA channels. Therefore, we will calculate analytically the change of the synaptic weight by correlating the deriva- tive of the membrane potential with the activity of the NMDA channel. Thus, for this calculation we utilise biophysical variables of the physi- ological cell. The final result shows a weight change curve which con- forms with measurements from biology. The positive part of the weight change curve is determined by the NMDA activation. The negative part of the weight change curve is determined by the membrane potential change. Therefore, the weight change curve should change its shape de- pending on the distance from the soma of the postsynaptic cell. We find temporally asymmetric weight change close to the soma and temporally symmetric weight change in the distal dendrite.

Structuralization of the covariance matrix reduces the number of parameters to be estimated from the training data and does not affect an increase in the generalization error asymptotically as both the number of dimensions and training sample size grow. A method to benefit from approximately correct assumptions about the first order tree dependence between components of the feature vector is proposed. We use a structured estimate of the covariance matrix to decorrelate and scale the data and to train a single-layer perceptron in the transformed feature space. We show that training the perceptron can reduce negative effects of inexact a priori information. Experiments performed with 13 artificial and 10 real world data sets show that the first-order tree-type dependence model is the most preferable one out of two dozen of the covariance matrix structures investigated.