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. 2021 Oct 27;11(1):21182.
doi: 10.1038/s41598-021-00516-y.

Role of NMDAR plasticity in a computational model of synaptic memory

Ekaterina D Gribkova  1   2 , Rhanor Gillette  3   4
Affiliations

Role of NMDAR plasticity in a computational model of synaptic memory

Ekaterina D Gribkova et al. Sci Rep. .

Abstract

A largely unexplored question in neuronal plasticity is whether synapses are capable of encoding and learning the timing of synaptic inputs. We address this question in a computational model of synaptic input time difference learning (SITDL), where N-methyl-d-aspartate receptor (NMDAR) isoform expression in silent synapses is affected by time differences between glutamate and voltage signals. We suggest that differences between NMDARs' glutamate and voltage gate conductances induce modifications of the synapse's NMDAR isoform population, consequently changing the timing of synaptic response. NMDAR expression at individual synapses can encode the precise time difference between signals. Thus, SITDL enables the learning and reconstruction of signals across multiple synapses of a single neuron. In addition to plausibly predicting the roles of NMDARs in synaptic plasticity, SITDL can be usefully applied in artificial neural network models.

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Conflict of interest statement

The authors declare no competing interests.

Figures

Figure 1
Figure 1
The SITDL hypothesis: An example of how activity-dependent changes in NMDAR population can affect synaptic current timing. (A) Left: A developing silent synapse starts with a majority of slow NMDARs with slower glutamate gate activation than fast NMDARs. The synapse receives a glutamate signal followed later by a dendritic voltage signal, causing a difference in activation of NMDARs’ voltage and glutamate gates. Right: As the synapse develops and experiences the same timing between voltage and glutamate signals, its NMDAR population may change, caused by the difference in glutamate and voltage gate activation. In this case, fast NMDARs replace slow NMDARs until the gate conductance difference is minimized, thus aligning the overall NMDAR current peak with the peak of the voltage signal. This allows the developing synapse to learn the timing difference between the voltage and glutamate signals by encoding it in the NMDAR population’s glutamate gate activation time. (B) Left: Each NMDAR has a glutamate gate and a voltage gate that can be activated independently, with corresponding gate conductances shown. Coincident activation of both gates allows influx of Ca2+ (NMDAR Current). A slow NMDAR has a slower glutamate gate activation, therefore experiencing slower change in glutamate gate conductance than a fast NMDAR. Right: Circuit diagram of a post-synaptic spine containing only NMDARs. An NMDAR (RNMDAR) is shown as variable serial resistances of its glutamate gate (RG) and voltage gate (RV) that depend on the glutamate signal (SGlu) and dendritic spine’s voltage (V), respectively. CM denotes the membrane capacitance, RM the membrane resistance, ECa2+ the cell’s Nernst potential for Ca2+, and I(t) the external input.
Figure 2
Figure 2
SITDL simulations of a single synapse receiving periodic inputs and showing evolution of τGlu and conductances for different initial conditions of τGlu and τD. In each case, the synapse receives a synaptic glutamate signal (light green) followed by a dendritic voltage signal (light blue) delayed by time τD. τGlu changes over time due to the NMDAR gate conductance mismatch. (A) Simulation with initial values τGlu = 5 ms and τD = 15 ms. Initially, glutamate gate conductance, gGlu, peaks before voltage gate conductance, gV. Over time, τGlu grows, delaying the gGlu peak and achieving greater coincidence. (B) Simulation with initial values τGlu = 50 ms and τD = 10 ms. In this case, gV initially peaks before gGlu. τGlu decreases over time, resulting in greater coincidence of the gate conductances. (C) Simulation with initial values τGlu = 50 ms and τD = 95 ms. Though there is much less overlap between glutamate and voltage signals, due to periodicity of the signal, the SITDL mechanism still appears to achieve greater coincidence over time.
Figure 3
Figure 3
SITDL simulations with and without stabilization mechanisms, under different sets of initial conditions. Each curve shows the changes in τGlu over time, for a single simulation with the specific initial τD value indicated by the color of the curve. (A) Changes in τGlu when starting with τGlu = 5 ms and different initial τD value for each curve, ranging from 1 to 17 ms. By 600,000 ms simulation time, each curve appears to reach more stable values. (B) Changes in τGlu with initial conditions τGlu = 5 ms and τD value ranging from 18 to 45 ms. In most cases, τGlu increases, but there does not appear to be sufficient simulation time for it to reach more stable values as in (A). (C) Changes in τGlu with initial conditions τGlu = 5 ms and τD value ranging from 46 to 100 ms, which provide much less overlap of glutamate and voltage signals. Certain τD values, such as 49 to 60 ms, 70 to 75 ms, and 90 to 100 ms, seem to provide sufficient overlap for τGlu to change significantly and potentially achieve coincidence of gate conductances with enough simulation time. (D–F) Same simulations and initial conditions as in Fig. 4A–C, but with stabilization mechanisms, which cause τGlu to stop changing when there is sufficient overall NMDAR conductance. Note, τGlu stabilization generally occurs more quickly for smaller τD, and even at high τD (18 to 100 ms), τGlu still stabilizes for certain values at the end of the simulation, despite limited overlap of the periodic signals. (G–I) Same simulations with stability mechanisms as in Figure (D–F), except with initial τGlu = 50 ms.
Figure 4
Figure 4
Simulation of the SITDL synapse model, showing changes in τGlu, and corresponding changes in numbers of slow and fast NMDARs. This simulation was run with plasticity and stabilization mechanisms for τGlu, with initial conditions τGlu = 150 ms and τD = 10 ms, and with constants for calculating the numbers of slow and fast NMDARs nTotal = 50, τFast = 7 ms, and τSlow = 50 ms. (A) Segments of 90 ms close to the start and end of the simulation are shown at the left and right, respectively, with gGlu and gV peaks (green and blue dashed lines) noticeably becoming more coincident. (B) shows the time course of τGlu, with an initial value of 150 ms (τSyn ≈ 30 ms), which corresponds to the synapse having 26 slow NMDARs and 24 fast NMDARs. τGlu decreases overall, with some oscillation, until it stabilizes at 12.7 ms (τSyn ≈ 11 ms), which corresponds to 5 slow NMDARs and 45 fast NMDARs in the synapse, indicating a replacement of slow NMDARs with fast NMDARs. (C) shows the corresponding numbers of slow and fast NDMARs over time, each averaged over a 800 ms time window (darker traces).
Figure 5
Figure 5
Multi-synaptic SITDL simulations of learning. (A) The Learning Phase starts with a large number of redundant synapses, each receiving the same periodic glutamate signal, delayed relative to a similarly periodic but sparse voltage signal by dendritic time constant τD. After learning, synapses are eliminated or stabilized based on overall NMDAR conductance. During the Recall Phase each mature stabilized synapse receives a single glutamate spike. The summation of resulting voltages across all stabilized mature synapses with the appropriate dendritic delays, produces a reconstruction of the original glutamate signal received during the learning phase. (B) Evolution of τGlu for synapses that were stabilized at the end of Learning Phase simulations. The full set of synapses started with initial conditions τGlu = 20 ms and τD values uniformly distributed from 4 to 100 ms, with a step of 2 ms. Synapses with insufficient average overall NMDAR conductance were eliminated, leaving only stabilized synapses, whose corresponding τD are shown. (C) An example of a Learning Phase simulation, showing how NMDAR conductances change over time for a synapse with initial τGlu = 20 ms and τD = 64 ms. The synapse receives a periodic glutamate signal and a sparse voltage signal with the same period. The first voltage spike occurs close to the fourth spike of the glutamate signal. At the end of the simulation the average overall NMDAR conductance is sufficient for this synapse to be stabilized. (D) Recall Phase simulation of stabilized synapse from (C) with final values τGlu = 5.0 ms and τD = 64 ms. Since stabilized synapses are assumed to express AMPARS, in this case the synapse receives a single glutamate spike coincident with a single voltage spike.
Figure 6
Figure 6
Results of Recall Phase simulations for synapses with and without SITDL mechanisms. There are 4 different sets of synaptic simulations, each with their own starting conditions: 2 sets of SITDL simulations with τD step = 2 ms and 8 ms, and 2 sets of simulations without SITDL mechanisms with τD step = 2 ms and 8 ms. For all simulation sets, τD values are initially distributed uniformly with the corresponding τD step, and all initial τGlu = 20 ms. For each simulation set, following Learning Phase simulations, synaptic elimination, and Recall Phase simulations, a recall signal is obtained by summating the resulting Recall Phase voltage signals (Fig. 5C), shifted by corresponding τD (A–D traces in color), over all stabilized synapses. Note, to provide better visual comparison of original and recall signals, the original signal was slightly shifted relative to the recall signal, with a delay of 5.5 ms for (A,D), and 5 ms for (B,C). (A) The recall signal for SITDL simulation set with τD step = 2 ms very closely resembles the original glutamate signal that was used during Learning Phase. (B) Recall signal for SITDL simulation set with τD step = 8 ms is less similar to the original glutamate signal, because of the much larger τD step used during Learning Phase. (C,D) Recall signals for no-SITDL simulation sets with τD step = 8 ms and 2 ms, respectively. There are no changes in τGlu in these simulations, thus synapses are unable to achieve greater overlap of glutamate and voltage gate conductances. Even with synapses that were stabilized, the peaks of the recall signal are significantly shifted from the peaks of the original glutamate signal. (E) Estimates of MI between original glutamate signal and recall signal for each simulation set, using MI estimator AIMIE. SITDL simulation sets, particularly the one with smaller τD step (2 ms), provide greater MI estimates than no-SITDL simulation sets, suggesting greater degree of similarity between their reconstructed recall signal and the original glutamate signal.
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