Figures and data
Reproduced from [3]. Dendritic NMDA-dependent action currents. (A) Long lived voltage transients can be initiated by NMDA receptors located within distal dendritic branches. (B) If the input to a dendritic branch with NMDA receptors is sufficiently strong, it can cross a threshold to produce an NMDA spike (middle trace). The NMDA response to inputs is super-linear, until it saturates in a plateau potential (top trace). (C) A somatic spike mediated by voltage-gated sodium channels. Note the order of magnitude difference in timescales with (b).
(A) Reproduced from [23]. Fluorescent dye fill image of a layer V pyramidal neuron recorded intracellularly in a rat cortical slice [23]. Two dendrites are marked where an NMDA spike is triggered through release of glutamate. (B) Voltage traces of the NMDA spikes of the dendritic patches marked in A. Note the long duration of the NMDA spike compared to the somatic sodium spikes evident in the top-left panel. (C) The morphology of the biophysical model used for simulating detailed NMDA plateau potentials. The arrows mark the positions where glutamate release was simulated. (D) The three traces of the NMDA spikes triggered at the sites marked in C, and the resulting somatic spike. (E) The morphology of the abstract model, with and without active NMDA dendrites. (F) The voltage traces of the abstract model, with and without plateaus. Because of the extended time duration of the plateau potentials, they are summed to reach threshold. In the case where the plateau potentials are absent, they do not sum due to the short membrane time-constant of the soma. (G) Voltage traces of a basal dendrite with an NMDA spike, in the biophysical model, with an increasingly strong inhibitory current added (left). The plateau duration decreases linearly for a linear increase in the inhibitory conductance (right).
(A) Neurons integrate inputs and compare the result to a firing threshold, which is comparable to performing a binary classification. When inputs are synchronous this can be done with a low number of spikes (left). But when spike timing is unpredictable (middle), this falls apart. Extended depolarizing potentials within dendritic compartments acts as a hold mechanism, allowing asynchronous events from different compartments to summate (right). (B) Simulation of summed voltage for 10 dendritic compartments, for small amounts of input-event timing jitter (on the order of one EPSP duration τ ∼ 10 ms; left), and larger amounts jitter (10τ, middle). Increased jitter increases the variability of the net depolarization. Extended depolarizing potentials on the duration of ∼ 20 ms reduce the variability in net depolarization. Voltage values were normalized by dividing by the maximum of the mean, and the shaded are shows the inner 90% of the resulting distribution of the voltage. (C) Increased jitter in the timing of input events reduces the net summed depolarization. (D) Increased jitter in the timing of input events increases the variability in membrane voltage depolarization. (E) Variability can be controlled by increasing the number of inputs, but this is not cost-effective.
A simple conductance based model displays the same qualitative behavior as a detailed biophysical model. (A) The classification task performed by the spiking network of figures D, E, F. Each point is a 2D input vector x, the colors represent the different classes. (B) Procedure of transforming continuous 2D inputs x into input spikes for the network. First, x is projected onto a binary feature space to obtain a binary vector in a higher dimensional space. Then, spike times are added to this binary vector to produce the series of input spikes. For details, see subsection 3.4. (C) Schematic of the network architecture. The input somas spike according to the spike times obtained from the binary input vector. Each soma in the next layer has one dendrite per upstream soma, and each dendrite is connected to both one downstream and one upstream soma only. The dendrite-soma coupling is a bidirectional passive resistive coupling, whereas the upstream somas have a one-directional synaptic coupling onto the dendrites. (D) Example of the spiking network equipped with plateaus in the dendrites receiving asynchronous input spikes. It classifies the three inputs correctly in spite of the asynchrony. (E) Example of the spiking network equipped with dendrites without plateaus receiving asynchronous input spikes. The first two points are classified incorrectly, the network gets the third answer correct. (F) Summary of how well the network with plateaus and the network without plateaus deal with asynchrony τ, with the performance measured as the percentage of points of the classification task classified correctly. Without plateaus the performance drops off quickly (dashed line), whereas the network with plateaus does not suffer from performance degradation for this range of τ (solid line).
