Calcium-Dependent Calcium Decay Explains STDP in a Dynamic Model of Hippocampal Synapses

Abstract

It is widely accepted that the direction and magnitude of synaptic plasticity depends on post-synaptic calcium flux, where high levels of calcium lead to long-term potentiation and moderate levels lead to long-term depression. At synapses onto neurons in region CA1 of the hippocampus (and many other synapses), NMDA receptors provide the relevant source of calcium. In this regard, post-synaptic calcium captures the coincidence of pre- and post-synaptic activity, due to the blockage of these receptors at low voltage. Previous studies show that under spike timing dependent plasticity (STDP) protocols, potentiation at CA1 synapses requires post-synaptic bursting and an inter-pairing frequency in the range of the hippocampal theta rhythm. We hypothesize that these requirements reflect the saturation of the mechanisms of calcium extrusion from the post-synaptic spine. We test this hypothesis with a minimal model of NMDA receptor-dependent plasticity, simulating slow extrusion with a calcium-dependent calcium time constant. In simulations of STDP experiments, the model accounts for latency-dependent depression with either post-synaptic bursting or theta-frequency pairing (or neither) and accounts for latency-dependent potentiation when both of these requirements are met. The model makes testable predictions for STDP experiments and our simple implementation is tractable at the network level, demonstrating associative learning in a biophysical network model with realistic synaptic dynamics.

Inferring Neuronal Dynamics from Calcium Imaging Data Using Biophysical Models and Bayesian Inference

“…More specifically, the presented approach is a first step towards incorporating the networks of biophysical spiking neuron models (e.g. see [ 116 , 117 ]), together with their ubiquitous mechanisms such as synaptic plasticity (e.g. see [ 117 – 119 ]).…”

“…see [ 116 , 117 ]), together with their ubiquitous mechanisms such as synaptic plasticity (e.g. see [ 117 – 119 ]). We expect that such a network extension enables studying the neuronal dynamics and biophysical parameters of complex neuronal circuits measured indirectly by calcium imaging.…”

Dendritic spine geometry and spine apparatus organization govern the spatiotemporal dynamics of calcium

“…It has long been considered that a neural circuit level model of synaptic weight updates can be informed by the calcium transients in the synapse. As a result, weighting functions have been proposed that consider calcium dynamics ( Cummings et al, 1996 ; Shouval et al, 2002 ; Yeung et al, 2004 ), and these functions have been used to connect biophysical features of NMDARs to synaptic weight updates in models of spike time-dependent plasticity (STDP; Sejnowski, 1977 ; Song et al, 2000 ; Izhikevich, 2007 ; Bush and Jin, 2012 ; Standage et al, 2014 ). We now propose that the calcium transient is explicitly a function of the spine volume-to-surface area, ultrastructure, and buffers, and that the calcium functions that inform the synaptic weight vectors and synaptic learning rate ( Fig.…”

Field‐Driven Athermal Activation of Amorphous Metal Oxide Semiconductors for Flexible Programmable Logic Circuits and Neuromorphic Electronics

“…In glutamatergic connections, strengthening/long‐term potentiation (LTP) occurs if the presynaptic spike precedes the postsynaptic spike ( t post–pre > 0, where δt is the relative time interval between the pre‐ and postsynaptic spikes), while presynaptic spikes following postsynaptic spikes ( t post–pre < 0) causes weakening/long‐term depression (LTD). In these devices, spike patterns corresponding to Figure S11 (Supporting Information) created interval‐dependent net voltage changes across the device, resulting in temporally manipulatable weight changes following an asymmetric anti‐Hebbian rule (Figure d and Figure S12a (Supporting Information)), and asymmetric Hebbian behavior (Figure S12b, Supporting Information) analogous to biological systems . For example, an interval ( t post–pre ) of +500 ms resulted in a net voltage of V pre − V post = (−0.75) − (+0.75) = −1.5 V developed across the device, triggering a permanent decrease in the channel conductance or LTD (≈22 %).…”

“…In these devices, spike patterns corresponding to Figure S11 (Supporting Information) created interval-dependent net voltage changes across the device, resulting in temporally manipulatable weight changes following an asymmetric anti-Hebbian rule (Figure 6d and Figure S12a (Supporting Information)), and asymmetric Hebbian behavior ( Figure S12b, Supporting Information) analogous to biological systems. [46,47] For example, an interval (t post-pre ) of +500 ms resulted in a net voltage of V pre − V post = (−0.75) − (+0.75) = −1.5 V developed across the device, triggering a permanent decrease in the channel conductance or LTD (≈22 %). On arrival of presynaptic pulses after postsynaptic pulses, i.e., t post-pre of −500 ms, the maximum net voltage developed across the device was V pre − V post = (+0.75) − (−0.75) = +1.5 V and this resulted in an increase in conductance or LTP (≈114 %).…”