Figure 1.
Receptor kinetics and open probability.
(A) The kinetic scheme used to model the receptors. O is the open state; D1 and D2 are desensitized; 0, 1, 2, C1 and C2 are closed. Rate constants, taken from Erreger et al. [21]. and adjusted for temperature, are listed in Table 2. (B,C) Time course of free glutamate concentration in the synaptic cleft. Glutamate concentration peaked and decayed rapidly; the initial τ of decay was ∼60 µsec. (D,E) Examples of single receptor opening and closing in response to glutamate release show that NR2A-containing receptors fail less often, and open and close more rapidly than NR2B-containing receptors. Note that the simulations were carried out at 33°C, so the receptor kinetics are significantly faster than those observed by Erreger et al. [21]. (F,G) Peak open probability was 10 times higher, the early decay component time constant was four times faster, and the probability of success a receptor opening in response to glutamate release (P(success)) was three times greater for NR2A-containing receptors than for NR2B-containing receptors.
Table 1.
Parameters used in simulation of glutamate diffusion.
Table 2.
Rate constants for NMDAR models.
Figure 2.
Time open and receptor failure.
(A,B) Upon opening, NR2B-containing receptors stayed open much longer than NR2A-containing receptors. The late decay component time constant was twice as slow, and the weighted time constant of decay (τw) was 10 times slower. (C) The probability of at least one receptor opening, given the number of receptors at the synapse, shows that very few NR2A-containing receptors are needed to provide near-perfect fidelity. (D) Total time open, given the number of receptors. Despite the fact that NR2A-containing receptors open three times as often, NR2B-containing receptors stay open longer, so total time open is only about 50 percent greater for NR2A-containing receptors.
Figure 3.
Estimating open probability using MK-801 block.
Simulation of an experiment that used brief pulses of glutamate and MK-801 to estimate the open probability of receptors given different NR2A/NR2B ratios [19]. The average behavior of NR2A and NR2B-containing receptors under this protocol was simulated using a probabilistic model. (A,B) The responses of NR2A and NR2B-containing receptors alone, showing the responses to glutamate alone (Control) and to the 1st and 5th stimulations. (C,D) The peak open probability upon successive stimulations, unnormalized (C) and normalized relative to the response to glutamate alone (D), showing that NR2A-containing receptors had a higher open probability, and were blocked more rapidly. (E–H) Same as above, but for two mixed populations of receptors. A population containing 80 percent NR2A-containing receptors had a higher open probability and was blocked more rapidly than a population containing 80 percent NR2B-containing receptors. However, when plotted relative to control (H), the block appeared very similar in the two cases. Similar results were observed for other mixed populations.
Figure 4.
Spatial pattern of receptor opening.
(A,B) Probability of opening (A) for NR2B-containing NMDARs nearly doubled, while increasing only modestly for NR2A-containing NMDARs for simultaneous release of two vesicles. Average time (B) open for NR2B-containing receptors was consequently greater. (C,D) The probability of receptor opening (C) and time open (D) versus the number of glutamate molecules released from a single vesicle increased linearly for NR2B-containing NMDARs up to 5000 molecules, at which point NR2A-containing NMDARs had already began to saturate. At 3000 molecules, the total time open for NR2B- was greater than for NR2A-containing NMDARs. (E,F) NR2A-containing NMDAR success probability (A) was nearly indifferent to location, while NR2B-NMDARs (B) showed a hot spot of success probability near the site of glutamate release. (G) The decrease in success probability with distance from the site of release for both synaptic (distance from release site<250 nm) and perisynaptic receptors.
Figure 5.
Triheteromeric receptors and the number of receptors at a synapse.
(A) The kinetic scheme used to model the triheteromeric receptors. Glutamate binding and unbinding to the NR2A and NR2B subunits was independent, thus there were two single-bound states (1A, 1B). Binding and unbinding rates for NR2A and NR2B were as in the previous models; all other rate constants were the geometric means of the values in the previous models (Table 2). (B) Opening and closing kinetics for our model triheteromeric NR2A/B-containing receptor. Open probability and decay kinetics were intermediate between the diheteromeric receptors, but more similar to those of NR2A-containing receptors. (C) Average number of each type of receptor present at the synapse, based on our simulations and the results of Nimchinsky et al. [26], under three different assumptions: that only diheteromeric NMDARs were present (AA, BB), that only NR2B- and NR2A/B-containing receptors were present (AB, BB) and that all three receptor types were present and combined randomly (AA, AB, BB). In all three cases, NR2B subunits made up greater than 85 percent of the subunit content at the synapse. There was no positive solution for the case where only NR2A and NR2A/B-containing receptors were present.
Figure 6.
Calcium influx in response to tetanic stimulation.
(A,B) LTP was induced by 100 Hz tetanic stimulation with a duration of 1 sec. The postsynaptic voltage (A) and stochastic glutamate release (B) were both modulated synaptic facilitation and depression. (C–F) Example postsynaptic calcium concentration traces (C,D) from simulations with 5 NR2A-containing or 5 NR2B-containing NMDARs, and mean calcium concentration in the spine in for three different numbers of receptors (E,F) show that NR2A-NMDARs drove spine calcium concentration much higher, per receptor, than did NR2B-NMDARs.
Figure 7.
Effects of NR2 subtype on long-term potentiation.
The synapse model was coupled to a model of postsynaptic potentiation, where CaMKII phosphorylation is the switch for LTP. (A–C) Sample traces of active CaMKII concentration for synapses with different numbers of each receptor type present (A,B) show that NR2A-containing receptors drove LTP more effectively, per receptor, than did NR2B-containing NMDARs (C). (D) The receptor open probability during the stimulation period was the main determinant of calcium influx. (E) The total time the receptors spent open during the stimulation was a good predictor of the probability a synapse would be potentiated. (F) Long-term potentiation via the triheteromeric receptors was also intermediate between NR2A- and NR2B-containing receptors but more similar to NR2A-containing NMDARs. (G) When glutamate release was paired with brief depolarizations of the postsynaptic cell at different temporal offsets, NR2A-containing receptors showed a much narrower temporal window for potentiation than did NR2B-containing receptors.