A tale of two stories: astrocyte regulation of synaptic depression and facilitation

Authors’ summary

• Astrocytes may increase or decrease overall synaptic release while changing the second response in paired stimuli in the opposite direction, transiently switching depression and facilitation.The model proposes these effects as a way to explain challenging experimental observations and alter synaptic information transfer.Source: Authors’ summary · p. 3

Introduction

• The study uses a biophysically plausible model to identify signaling-dependent parameter regimes in which astrocytes can switch synapses between facilitating and depressing responses.The authors propose this mechanism as a possible explanation for contradictory experimental evidence.Source: Introduction · pp. 4–5

The road map of astrocyte regulation of presynaptic short-term plasticity

• Astrocyte-released glutamate can bind presynaptic receptors and alter presynaptic Ca2+ influx and release; the model focuses on non-homosynaptic signaling and the timing of glutamate release.Astrocytic Ca2+ may be driven by another synapse, neighboring astrocytes, external stimulation, or spontaneous activity.Source: The road map of astrocyte regulation… · pp. 6–7

The Tsodyks-Markram model of a dynamical synapse

• The Tsodyks-Markram model represents synaptic resources as a limited pool depleted by release and replenished over time, while release probability reflects Ca2+-sensor occupancy.Incoming spikes increase sensor occupancy, which recovers between spikes.Source: The Tsodyks-Markram model of a… · p. 7

Mechanisms of short-term presynaptic plasticity

• In the model, U0 above its threshold produces depression, whereas U0 below threshold permits facilitation at some input frequencies before depression emerges.Spike frequency and timing shape responses: low-frequency stimulation can increase release, while high-frequency stimulation depletes available resources and reduces it.Source: Mechanisms of short-term presynaptic… · pp. 8–9

Modeling the action of the astrocytic glutamate on synaptic release

• The astrocyte model treats Ca2+-triggered glutamate release as drawing on a replenishing resource pool, with receptor occupancy Γ modulating basal synaptic release probability U0.The modulation is represented as a first-order function of Γ, with α capturing the effect of presynaptic receptor activation.Source: Modeling the action of the astrocytic… · pp. 10–11

Astrocyte can either depress or facilitate synaptic neurotransmitter release

• For α = 0, astrocytic glutamate decreases steady-state release at 0.1–10 Hz and creates a facilitating peak-frequency response that gradually returns toward baseline.The model also predicts that the limiting frequency rises sharply after glutamate release and then relaxes.Source: Astrocyte can either depress or… · pp. 12–13
• Astrocytic glutamate transiently decreases release when α = 0 or increases it when α = 1, with responses slowly recovering toward control.The effect parameter α summarizes the density and biophysical properties of the presynaptic receptors targeted by astrocytic glutamate.Source: Astrocyte can either depress or… · p. 13

Modulation of paired-pulse plasticity by astrocytic glutamate

• Release-decreasing astrocytes shifted depressing synapses toward paired-pulse facilitation, whereas release-increasing astrocytes shifted facilitating synapses toward depression.The shifts appeared both in Poisson-train paired-pulse measurements and in paired-pulse stimulation.Source: Modulation of paired-pulse plasticity… · pp. 14–15

Theoretical explanation of astrocyte-mediated transitions between PPD and PPF

• The opposite paired-pulse shifts coexist with global efficacy changes because astrocytic glutamate shifts release probability and the limiting frequency relative to facilitation conditions.Facilitation requires U0 < Uthr and fin < flim; astrocytic modulation can change whether these conditions hold, producing transitions between PPD and PPF.Source: Theoretical explanation of… · pp. 16–17

the astrocyte

• Ca2+ oscillation patterns shape glutamate-release timing: FM oscillations trigger release each cycle, whereas amplitude-gated AM and AFM oscillations produce variable release frequencies.AM oscillations at constant frequency can yield glutamate-release events of identical magnitude but variable frequency, so oscillation patterns may be encoded mainly by release frequency rather than magnitude.Source: plasticity · p. 17, the astrocyte · p. 18

Astrocyte regulates transitions between facilitation and depression

• Higher glutamate-release event rates strengthen facilitation at depressing synapses with release-decreasing astrocytes, but strengthen depression at facilitating synapses with release-increasing astrocytes.Above a critical event rate, release-increasing astrocytes can shift facilitating synapses into depression; release-decreasing astrocytes can shift depressing synapses into facilitation only when input frequency is below the synaptic limiting frequency.Source: Astrocyte regulates transitions… · pp. 18–20

Discussion

• Astrocytic glutamate signaling can switch synaptic plasticity modes, potentially changing spike-train filtering and information transfer.The model’s implications may extend to groups of synapses with shared or locally synchronized astrocytic Ca2+ dynamics, while effects on circuit information flow remain to be investigated; altered short-term plasticity could also affect STDP, but this requires further study.Source: Discussion · pp. 20, 23
• Lower astrocytic effect parameter α decreases overall synaptic release while increasing PPF; higher α increases release while enhancing PPD.The model also accounts for observations that astrocyte-mediated release facilitation correlates with a decreased paired-pulse ratio.Source: Discussion · pp. 20–21
• When α equals the terminal’s basal release probability U0*, opposing astrocyte-mediated depression and facilitation cancel, producing no net observable modulation of synaptic transmission.The model offers this as a possible explanation for reported cases in which Ca2+-dependent astrocytic glutamate release did not affect synaptic function.Source: Discussion · p. 21
• The model predicts that astrocyte-driven transitions between PPD and PPF depend on glutamate-release frequency and the synapse’s presynaptic signaling pathway.The predicted threshold for Ca2+ oscillations lies within the range of spontaneous astrocytic oscillations below 2.5 min-1, suggesting a possible role in basal synaptic release regulation.Source: Discussion · p. 22

• The Supporting Text is introduced as having an organization described in following material.Source: SUPPLEMENTARY TEXT S1 · p. 32

1. The Tsodyks-Markram model of synaptic release

• The synaptic-release component is the Tsodyks-Markram model.Source: §I · p. 32

2. Astrocytic calcium dynamics

• The model includes astrocytic calcium dynamics.Source: §I · p. 32

3. Glutamate exocytosis from the astrocyte

• The model includes glutamate exocytosis from the astrocyte.Source: §I · p. 32

4. Glutamate time course in the extrasynaptic space

• The model describes the glutamate time course in the extrasynaptic space.Source: §I · p. 32

5. Astrocyte modulation of synaptic release

• The model addresses astrocyte modulation of synaptic release.Source: §I · p. 32

Mechanisms of short-term depression and facilitation in the TM model of synaptic release

• The analysis first treats mechanisms of short-term depression and facilitation in the Tsodyks–Markram model of synaptic release.Source: §II · p. 32

Characterization of paired-pulse depression and facilitation

• A separate subsection characterizes paired-pulse depression and facilitation.Source: §II · p. 32

Mean-field description of synaptic release

• The analysis develops a mean-field description of synaptic release.Source: §II · p. 32

Frequency response and limiting frequency of a synapse

• It also examines synapse frequency response and limiting frequency.Source: §II · p. 32

Mean-field description of astrocyte-to-synapse interaction

• A further mean-field subsection addresses astrocyte-to-synapse interaction.Source: §II · p. 32

Appendix A: Model equations

• Appendix A presents the model equations.Source: §II · p. 32

Appendix B: Estimation of the coefficient of variation of Γ

• Appendix B concerns estimation of the coefficient of variation of Γ.Source: §II · p. 32

Appendix C: Parameter estimation

• Appendix C concerns parameter estimation.Source: §II · p. 32

1. The Tsodyks-Markram model of synaptic release

• The Tsodyks–Markram model represents short-term depression and facilitation through variables u, the Ca2+ sensor occupancy, and x, the fraction of glutamate available for release.The variables respectively correlate with sensor occupancy and glutamate availability.Source: §1 · p. 33
• After a presynaptic spike increases u, the released glutamate amount is ux, while the available glutamate pool recovers between spikes.The pool is assumed to be constant in size.Source: §1 · p. 33
• The model treats x as vesicle availability, u as release probability for a docked vesicle, and RR as release probability per site; it reproduces average release, not stochastic events.At very low stimulation frequency, U0 can be regarded as basal release probability.Source: §1 · pp. 33–34

2. Astrocytic calcium dynamics

• Astrocytic intracellular Ca2+ dynamics arise through several mechanisms, with IP3-dependent Ca2+-induced Ca2+ release from the ER considered the primary mechanism; its nonlinear channels produce oscillations.Ca2+ oscillations may encode IP3 concentration through amplitude, frequency, or both [76-17].Source: §2 · p. 34
• The model represents astrocytic Ca2+ encoding with stereotypical amplitude-modulated (AM), frequency-modulated (FM), or combined (AFM) oscillations [76-17].The oscillation frequency and phase are fC and φC, while positive even-integer exponent w adjusts the waveform from sinusoidal to pulse-like.Source: §2 · p. 34
• The model externally drives IP3 through gap-junction diffusion from neighboring astrocytes or external stimulation, controlling Ca2+ patterns while retaining essential IP3/Ca2+-coupled signaling features [23-25, 18, 32-59, 74, 73].The modulation functions depend on astrocyte properties, and the model uses analogous forms linked to IP3 concentration above a CICR threshold.Source: §2 · p. 35

3. Glutamate exocytosis from the astrocyte

• Although IP3-triggered Ca2+ release induces astrocytic glutamate exocytosis, evidence for RyR-mediated Ca2+ signaling is contradictory, so the model excludes it.Source: §3 · p. 35
• Astrocytes have regulated glutamate vesicles resembling excitatory synaptic vesicles, and express SNARE and vesicular glutamate-sequestering proteins,,,.Source: §3 · p. 35
• Observed astrocytic vesicle fusion, trafficking, recycling, quantal release, and faster release than reintegration support the synaptic analogy,,, [62],.Source: §3 · p. 35
• The model represents astrocytic glutamate release as depletion of a finite releasable pool by U_Ax_A, followed by reintegration at rate Ω_A.The pool is assumed constant in size; release occurs upon a proper intracellular Ca2+ increase.Source: §3 · p. 36
• Release is triggered only when intracellular Ca2+ crosses a threshold while rising; oscillations trigger synchronous release, whereas sustained increases induce release only during their initial rise, [63, 59].The model uses the Ca2+ dynamics described by equations (4–6) to determine release times.Source: §3 · p. 36
• Each Ca2+ rise beyond threshold is modeled as one release event regardless of whether one or multiple vesicles contribute; asynchronous release with fast glutamate clearance could make this simplification inaccurate,.The authors note that further experiments are needed to support the asynchronous-release possibility.Source: §3 · p. 36

4. Glutamate time course in the extrasynaptic space

• The model represents extrasynaptic glutamate concentration as astrocytic release minus losses from diffusion and transporter uptake.Detailed spatial modeling is outside the study’s scope.Source: §4 · p. 36
• Astrocytic glutamate is released instantaneously at Ca2+ threshold crossings, with total release formed by summing contributions from individual events.Each event releases a fraction of the astrocyte’s releasable glutamate resources.Source: §4 · pp. 37–38
• Diffusion is modeled as proportional to extrasynaptic glutamate concentration, while transporter uptake follows Michaelis–Menten kinetics.The diffusion term assumes an isotropic extrasynaptic space; uptake depends on maximal uptake rate and transporter affinity.Source: §4 · p. 38
• Under the assumption that transporters are unsaturated, uptake is approximately linear in glutamate concentration and extrasynaptic glutamate decays monoexponentially.The resulting overall clearance rate combines uptake and diffusion.Source: §4 · pp. 38–39
• The model treats transporters as glutamate sinks and neglects uptake-driven replenishment of releasable astrocytic resources, assuming replenishment occurs independently of extracellular glutamate.The passage notes that uptake-derived glutamate is largely metabolized, while vesicular glutamate can be synthesized from glucose or amino acids; the role of uptake-derived α-ketoglutarate remains unresolved.Source: §4 · p. 39

5. Astrocyte modulation of synaptic release

• Astrocytic glutamate acts on pre-terminal glutamate receptors, with mGluRs linked to depression and NR2B-containing NMDA receptors or group I mGluRs implicated in facilitation.Proposed mechanisms include mGluR inhibition of P/Q-type Ca2+ channels, Ca2+ influx through NR2B-containing NMDARs, and ryanodine-sensitive Ca2+-induced Ca2+ release.Source: §5 · p. 40
• The model assumes astrocytic regulation changes U0, the release probability of docked vesicles, because this is consistent with presynaptic residual-Ca2+ effects and activity-independent modulation.It represents astrocytic glutamate’s effect through U0 = U0(GA), rather than adding an activity-dependent term.Source: §5 · p. 41
• The model introduces Γ phenomenologically in the context of astrocytic-glutamate effects on synaptic release, which may last tens of seconds up to minutes; Γ decays exponentially at rate ΩG, which must be small to mimic this long-lasting effect.Under the hypothesis that presynaptic Ca2+ levels are proportional to receptor occupancy, Γ biophysically correlates with the fraction of receptors bound to astrocyte-released glutamate.Source: §5 · pp. 41–42
• The model’s receptor-dependent parameter α captures release-decreasing, release-increasing, or mixed astrocyte effects through changes in basal release probability U0(Γ).For 0 < α < U0*, release decrease predominates; for U0* < α < 1, release increase predominates.Source: §5 · p. 43
• The model permits receptor-mediated modulation of release across receptor types, including presynaptic NR2B-containing NMDARs, which are described as lacking the postsynaptic voltage-dependent Mg2+ block.Receptor types are represented by differing rates ΩG and ΩG.Source: §5 · p. 43

model of synaptic release

• The TM model can mimic depressing or facilitating synapses depending on presynaptic spike frequency and Ωd, Ωf, and U0.Source: model of synaptic release · p. 44
• Depression is associated with reduced release probability, often through depletion of ready-releasable vesicles or reduced presynaptic Ca2+ influx; facilitation is associated with increased residual Ca2+ and release probability.Source: model of synaptic release · p. 44
• When spike frequency exceeds the glutamate-recovery rate Ωd, successive spikes deplete releasable glutamate and release progressively less, producing depression.Each presynaptic spike decreases available glutamate; the pool recovers at rate Ωd.Source: model of synaptic release · p. 44
• Depression begins more strongly at higher basal release probability U0 because glutamate depletion is then deeper.Source: model of synaptic release · p. 44
• When spike frequency exceeds the recovery rate Ωf, release probability grows across incoming spikes and facilitation occurs.After each spike, release probability is augmented by U0(1-u) and recovers toward baseline U0 at rate Ωf.Source: model of synaptic release · p. 44
• Facilitation and depression interact: stronger facilitation raises u and strengthens depression, so sufficiently long facilitating spike trains eventually depress release.Source: model of synaptic release · pp. 44–45

2. Characterization of paired-pulse depression and facilitation

• At rest, PPR > 1 marks paired-pulse facilitation (RR2 > RR1), whereas PPR < 1 marks paired-pulse depression (RR2 < RR1).PPR is the ratio of the second release event to the first.Source: §2 · p. 45
• In spike trains, PPRi alone cannot distinguish depression from facilitation because prior activity sets synaptic state; resource recovery can yield PPRi > 1 even as release probability falls.This recovery-from-depletion mechanism is distinct from both facilitation and depression.Source: §2 · pp. 45–46

3. Mean-field description of synaptic release

• The mean-field approach describes average synaptic dynamics for inputs sharing the same statistics without solving an equally large number of equations for each input.The passage attributes the approach to prior work [51, 57].Source: §3 · p. 46
• Averaging trials with identical initial conditions yields synaptic dynamics in terms of the trial means of u and x.The setup considers N presynaptic spike trains of the same duration.Source: §3 · p. 47
• Under the Poisson-input assumption, time averaging treats u, ux, and spike counts as independent and replaces the average spike count with the input firing rate.The averaging window is several interspike intervals long but shorter than the system’s longest timescale.Source: §3 · p. 47
• The closure approximation factors the average of ux into the product of the averages of u and x, despite their shared dependence on presynaptic spikes.For the cases studied, the self-consistency check based on the product of their coefficients of variation indicates an error no greater than 10%.Source: §3 · p. 48

4. Frequency response and limiting frequency of a synapse

• The mean-field model yields an analytical steady-state frequency response of released synaptic resources as a function of average input frequency.This response is used to characterize synaptic facilitation and depression.Source: §4 · pp. 48–49
• A negative frequency-response slope indicates depression, whereas a positive slope indicates facilitation.The slope is considered as input frequency increases.Source: §4 · p. 49
• When initial release probability U0 is below Uthr, a synapse can facilitate; when U0 exceeds Uthr, it is depressing.Uthr is the threshold value of U0 that determines the low-frequency slope.Source: §4 · p. 49
• A depressing synapse has maximal response as input frequency approaches zero, then declines monotonically toward zero; its cutoff marks attenuation greater than 3 dB.The cutoff frequency marks the onset of depression.Source: §4 · p. 49
• A facilitating synapse has a bell-shaped response with a peak frequency, as facilitation and depression coexist and depression dominates above the peak.Below the peak, the response slope is positive; at the peak, facilitation and depression compensate.Source: §4 · p. 49
• Facilitation occurs if and only if U0 < Uthr and input frequency is below the limiting frequency flim.The limiting frequency is the cutoff for a depressing response or the peak frequency for a facilitating response.Source: §4 · p. 50

5. Mean-field description of astrocyte-to-synapse interaction

• Assuming astrocytic glutamate exocytosis is Poisson-distributed, the model derives mean-field dynamics linking Ca2+-oscillation frequency to synaptic basal release probability.The passage motivates this assumption with evidence that spontaneous Ca2+ oscillations may be Poisson-like and that most oscillations can trigger exocytosis.Source: §5 · pp. 50–52
• The mean-field approximation’s relative error does not exceed about 7% in the cases studied.The estimate uses a Cauchy–Schwarz bound and is reported alongside Figure S7B.Source: §5 · p. 52

1.1. Conditioning IP3 signal

• The conditioned IP3 and Ca2+ signals include constant components, while the Ca2+ signal can incorporate AM and FM features and has frequency fC.The passage defines fC as the frequency of Ca2+ oscillations and the AM/FM parameters as binary switches.Source: §1.1 · p. 53

2.1. Glutamate exocytosis

• Astrocytic glutamate vesicle release is triggered when Ca2+ crosses threshold, with vesicle availability, basal release probability, and recovery rate governing release.The model denotes these quantities as xA, UA, and ΩA, respectively.Source: §2.1 · p. 53

2.2. Glutamate time course in the extracellular space

• Released astrocytic glutamate enters the extracellular space, where its concentration is shaped by diffusion clearance and transporter uptake.Release depends on available astrocytic vesicles and their release probability; Ωc denotes the overall clearance rate.Source: §2.2 · p. 54

3. Presynaptic receptors

• Presynaptic receptor occupancy Γ changes with astrocyte modulation, governed by onset rate OG and recovery rate ΩG.Source: §3 · p. 54

4. Synaptic release

• Synaptic release is modeled using basal probability U0, available vesicle fraction x, per-spike usage u, and astrocyte effect parameter α.The listed parameters also include the astrocyte-free basal probability U0*, vesicle recovery rate Ωd, and facilitation rate Ωf.Source: §4 · p. 55

Appendix B: Estimation of the coefficient of variation of Γ

• The approximation assumes slow Ca2+ oscillations and fast onset and glutamate clearance relative to recovery, so early modulation is governed mainly by glutamate release and receptor binding.Astrocytic glutamate is treated as nearly equal-magnitude quantal releases.Source: Appendix B · p. 56
• A recurrence for successive Γ peaks combines decay between release events with the contribution of each event; at steady state it estimates Γ and its second moment for cΓ.The recurrence is derived using the peak response and its decay before the next astrocytic glutamate release.Source: Appendix B · p. 57
• The mean inter-event decay factor is obtained by averaging exponential decay over exponentially distributed intervals in a Poisson glutamate-release train.The intervals are set by the event rate fC.Source: Appendix B · p. 57
• Roughly up to ~10% error was introduced in estimating cΓ over the studied Ca2+ oscillation range of 0.01–1 Hz.The appendix reports this from comparing equation (A6) with equation (49) (Figure S8).Source: Appendix B · p. 57

Synaptic parameters

• Reported hippocampal release probabilities generally span ~0.09–0.6, while vesicle recovery is typically 0.5–1 Hz and facilitation rates can range from 0.5 to 2 Hz or higher.The release-probability estimates are generally lower at facilitating synapses; faster vesicle recycling and facilitation rates are also reported.Source: Appendix C · p. 58

Astrocytic calcium dynamics

• The model normalizes astrocytic Ca2+ and IP3 to 0–1 with C0 = Ib = 0, and uses Cthr ≈ 0.13–0.8, evoked oscillation frequencies of ~0.01–0.1 Hz, and k = 1.The threshold range is inferred from reported thresholds of ~125–850 nM and stimulated peaks that can reach 1 μM or beyond.Source: Appendix C · p. 58

Astrocytic glutamate exocytosis

• Borrowing the synaptic rationale that docked astrocytic vesicles approximate readily releasable ones, the available pool is ~1–6 vesicles; estimated basal exocytosis release probability UA is <0.13.A single Ca2+-increase can reduce process vesicle numbers to 18 ± 14% of their original value; under a single-exocytotic-event approximation, this sets an upper UA limit of 0.82 ± 0.14. Multiple releases likely occur in observed Ca2+-dependent exocytosis, hinting UA could be smaller.Source: Appendix C · p. 59

Glutamate time course

• Glutamate clearance is estimated at Ωc ≈ 80 s-1 from decay within 100 ms, or ≈ 150 s-1 from a diffusion-only estimate; uptake, which could increase clearance, is not explicitly modeled.Transporter saturation is considered unlikely, supporting a monoexponential glutamate decay approximation.Source: Appendix C · pp. 60–61

Astrocyte modulation of synaptic release

• Astrocyte-mediated modulation may peak within 1–5 s and persist for tens of seconds to 2–3 min, corresponding to an estimated recovery rate ΩG below 0.5–1.2 min-1.A single Ca2+ increase has been reported to increase release by ~150–200%, while early in-vitro evidence suggests modulation could reach ~10-fold.Source: Appendix C · p. 61
• Assuming maximal depression of about 20% and minimal facilitation of 120% of resting U0*, the passage constrains Γ to 0.2 < Γ < 0.8 and OG to about 0.4 < OG < 2.From U0* = 0.5, astrocyte action could increase release probability at most twofold.Source: Appendix C · pp. 61–62