Bidirectional coupling between astrocytes and neurons mediates learning and dynamic coordination in the brain: a multiple modeling approach

Abstract

In recent years research suggests that astrocyte networks, in addition to nutrient and waste processing functions, regulate both structural and synaptic plasticity. To understand the biological mechanisms that underpin such plasticity requires the development of cell level models that capture the mutual interaction between astrocytes and neurons. This paper presents a detailed model of bidirectional signaling between astrocytes and neurons (the astrocyte-neuron model or AN model) which yields new insights into the computational role of astrocyte-neuronal coupling. From a set of modeling studies we demonstrate two significant findings. Firstly, that spatial signaling via astrocytes can relay a "learning signal" to remote synaptic sites. Results show that slow inward currents cause synchronized postsynaptic activity in remote neurons and subsequently allow Spike-Timing-Dependent Plasticity based learning to occur at the associated synapses. Secondly, that bidirectional communication between neurons and astrocytes underpins dynamic coordination between neuron clusters. Although our composite AN model is presently applied to simplified neural structures and limited to coordination between localized neurons, the principle (which embodies structural, functional and dynamic complexity), and the modeling strategy may be extended to coordination among remote neuron clusters.

Figure 1. A Tripartite Synapse.

The axon and dendrite, which are involved with the release and postsynaptic action of neurotransmitter respectively, are also connected to an astrocyte process which is sensitive to neurotransmitter. In response to neuronal neurotransmitter release the astrocyte can release further neurotransmitter (called gliotransmitter) which regulates the Excitatory Post-Synaptic Current (EPSC) generated by the postsynaptic neuron.

Figure 2. AN Model Block Diagram showing interactions between an astrocyte and neuron cell.

Figure 3. Network consists of presynaptic neuron A, postsynaptic neuron B and an interconnecting tripartite synapse.

AN model is used for signaling between the tripartite synapse and astrocyte.

Figure 4. Range of input frequencies producing Ca²⁺ oscillations for each mode of operation.

The valid ranges of input stimulus frequency which result in sustained Ca²⁺ oscillations are 5–17 Hz for AM, 9–35 Hz for FM and 1–10 Hz for AM-FM.

Figure 5. Supervised learning at S2.

Network consists of pre-synaptic neurons N1 and N3, post-synaptic neurons N2 and N4 and the interconnecting astrocyte. S1 communicates bi-directionally by releasing neurotransmitter (NT) and receiving gliotransmitter (GT) while S2 only receives GT from the astrocyte.

Figure 6. Synaptic Plasticity in the AN Model.

(A) Ca²⁺ oscillation resulting from pre-synaptic stimulation of S1 by N1, including the gating function f (red) and Ca²⁺ threshold (dashed). (B) neurotransmitter (y) released by S2 as a result of pre-synaptic stimulation by N2. Note how y is modulated by f due to glutamate release by the astrocyte when Ca²⁺ levels cross the threshold from below, targeting and binding with presynaptic mGluRs. (C) NMDA-mediated SICs induced by the release of glutamate from the astrocyte when Ca²⁺ levels cross the Ca²⁺ threshold. (D) PSC (Post-Synaptic Currents) comprising EPSCs and SICs). The EPSCs in S2 are generated as a result of the neurotransmitter released by S2 scaled by the weight of the synapse (ω) (see F). (E) N4 output firing activity (o/p). As long as the weight of S2 remains too low, N4 is only capable of firing when the astrocyte induces an NMDA current driven by the ‘supervisory’ input of N1. However this firing promotes STDP by allowing N4 to fire and therefore S2 is potentiated (see F). From ∼45 s onward the synapse is strong enough to cause firing also as a result of the pre-synaptic activity of N3. At ∼115 s the weight quickly grows uncontrollably and the neuron begins to fire rapidly.

Figure 7. Synaptic Plasticity in the AN Model (last 15 s).

(A) Ca²⁺ oscillation resulting from pre-synaptic stimulation of S1 by N1, including the gating function f (red) and Ca²⁺ threshold (dashed). (B) neurotransmitter (y) released by S2 as a result of presynaptic stimulation by N2. Again note how the amplitude of y is modulated by f. (C) SIC induced by the release of glutamate from the astrocyte when Ca²⁺ levels cross the Ca²⁺ threshold at ∼120.4 s. The kinetics of this SIC are similar to those observed in CA1 neurons . (D) PSCs at S2, comprising EPSCs elicited by the neurotransmitter released by N2 and the SIC. (E) N4 output firing activity. (F) Synaptic weight (ω). At ∼115 s the synapse is strong enough to cause firing as a result of the presynaptic activity of N3 without the aid of NMDA induced SICs.

Figure 8. Synaptic Plasticity in the AN Model (2.35 s–2.55 s).

(A) Ca²⁺ oscillation resulting from pre-synaptic stimulation of S1 by N1, including the gating function f (red) and Ca²⁺ threshold (dashed). (B) neurotransmitter (y) released by S2 as a result of presynaptic stimulation by N2. (C) SIC induced by the release of glutamate from the astrocyte when Ca²⁺ levels cross the Ca²⁺ threshold (crossing point not shown). (D) PSCs at S2, comprising EPSCs elicited by the neurotransmitter released by N2 and the SIC. (E) N4 output firing activity. (F) Synaptic weight (ω), Note that the weight either potentiates or depresses based on the temporal order of the pre and post neural activity.

Figure 9. Dynamic coordination in the AN model.

All synapses connected to the astrocyte can communicate via bidirectional signaling of neurotransmitter (NT) and gliotransmitter (GT).

Figure 10. Ca²⁺ oscillations and resulting coordination.

(A) Ca²⁺ oscillations (black line) and IP₃ levels (red line) at a synapse from N1 stimulated by 7 Hz Poisson spike train for 100 s. (B) Ca²⁺ oscillations at a synapse from N2 which is only stimulated from 0–40 s and 80–100 s with a 7 Hz Poisson spike train. (C) Activity of the gating function f which is activated when the total level of Ca²⁺ (D) within the astrocyte passes the threshold (D-black dashed line). (E and F) The output firing activity of neurons N1 and N2. Note that when the total Ca²⁺ oscillation crosses the threshold from below both neurons fire with a significantly higher frequency of activity; a result of the global release of glutamate and NMDA SIC activation. These are the only times that the neurons are highly coordinated. Furthermore it can be seen that there are extended periods of silence from both neurons after firing in bursts. This is a result of the negative feedback from f which depresses the release of neurotransmitter from the synapses and remains active until the Ca²⁺ oscillation crosses the threshold from above.

Figure 11. Coordinated firing activity of N1 and N2 for the first 15 s of AN model simulation.

(A) The aggregate level of Ca²⁺ (black line) and gating function f (red line). (B) and (D) firing activity of N1 and N2. (C) and (E) firing activity of N1 and N2 plotted as number of output spikes against time. When the level of Ca²⁺ crosses the threshold (1^st vertical dashed line) SIC stimulates all synapses causing each neuron to burst for approximately 600 ms (2^nd vertical dashed line). During this time the gating function f depresses neurotransmitter release from all synapses, during which the neurons are held silent as a result of decreased neurotransmitter release, until the Ca²⁺ level crosses the threshold from above (3^rd vertical dashed line) after which it takes approximately 1 s for the gating function to fully stop synaptic depression (4^th vertical dashed line). When this period ends the neuron can again fire as the synapses are releasing transmitter fully.

Figure 12. Example of total Ca²⁺ oscillations and neural coordination with different Ca²⁺ threshold levels.

(A) Ca²⁺ threshold (dashed line) set at 3.94 µM. (B) Neural activity of N1 (black) and N2 (red) plotted as number of spikes against time with the Ca²⁺ threshold set at 3.94 µM. (C) Ca²⁺ threshold set at 1.44 µM. (D) Same as (B) except that the Ca²⁺ threshold is 1.44 µM. The input stimuli to the synapses for both simulations are set at 7 Hz. When the threshold is too high (A) there is no crossing of the threshold by the total level of Ca²⁺. Since there is no astrocytic global release of glutamate, f is not activated and there is no coordinating bursting of the neurons (B). In contrast, where the threshold is crossed (C) and (D), f is activated and NMDA SICs are induced (not shown) thus producing coordinated activity of N1 and N2. Note that in both cases there is a reduction in total Ca²⁺: N2 produces no firing activity because the N2 synapse receives no stimulus between 40 s and 80 s.

Figure 13. Threshold variations vs the onset of coordination.

(A1) Total Ca²⁺ level and Ca²⁺ threshold (dashed line, 3.94 µM). (A2) f function. (A3) Spiking activity (o/p) of N1. (B1–B3) same as (A1–A3) with Ca²⁺ threshold set at 1.44 µM. Notice how the onset of bursting and the f function is delayed when the threshold is set at 3.94 µM since more time is required for the total Ca²⁺ level to cross the threshold. Furthermore, f is activated for a shorter period thereby reducing the duration of the silent period between bursts. Note that N2 bursts at the same time as N1 (data not shown).

Figure 14. Loss of Ca²⁺ oscillation in the synaptic microdomain.

(A) Ca²⁺ oscillation (black) and IP₃ levels (red) within a synaptic microdomain of N1. (B) Ca²⁺ oscillation and IP₃ levels within a synaptic microdomain of N2. (C) Total Ca²⁺ level within the astrocyte as a result of all synaptic microdomain oscillations and the f function (blue).(D) Neural output of N1 (black) and N2 (red) as spike count as a function of time. Since the threshold is close to the peak of the total Ca²⁺ oscillation f is only active for a short period. Therefore the reduction of IP₃ due to synaptic neurotransmitter release depression cannot prevent IP₃ levels reaching a point at which the sustained Ca²⁺ oscillations cease at synapses associated with N1. This is not the case at synapses associated with N2 as there is no synaptic input stimulation between 40 s and 80 s and IP₃ levels degrade naturally. Furthermore, the coordinated activity also changes: between 40 s and 80 s there is no bursting activity in either neuron since the total Ca²⁺ level is insufficient to cross the threshold.

Figure 15. Individual Ca²⁺ oscillations and IP₃ levels in AM mode.

(A–H) Individual Ca²⁺ oscillations (black), IP₃ transients (red) in each of the 8 microdomains associated with the synapses of N1 (A–D) and N2 (E–H). The input stimulus to each microdomain is a Poisson spike train with an average frequency of (A) 5 Hz, (B) 9 Hz, (C) 15 Hz, (D) 6 Hz, (E) 10 Hz, (F) 12 Hz, (G) 8 HZ, (H) 7 Hz. Note how the phase of the individual oscillations change, especially in (A), (D) and (H). Note also that the oscillation of IP₃ occurs at the same time for all microdomains. This is a result of the f function triggered by total Ca²⁺ which regulates the release of neurotransmitter at all synapses. It is the global oscillation of IP₃ that causes the phase shift of the individual Ca²⁺ oscillations.

Figure 16. Total Ca²⁺ oscillation and neural firing activity in AM mode.

(A) Total Ca²⁺ oscillation and Ca²⁺ threshold (dashed line). (B) f function. (C) Neural firing activity of N1. (D) Neural firing activity of N2. Note how total Ca²⁺ is much more sinusoidal than in previous experiments and that coordinated bursting of N1 and N2 occurs each time Ca²⁺ crosses the threshold from below.

Figure 17. Individual Ca²⁺ oscillations and IP₃ levels in AM-FM mode.

(A–H) Individual Ca²⁺ oscillations (black), IP₃ transients (red) in each of the 8 microdomains associated with the synapses of N1 (A–D) and N2 (E–H). The input stimulus to each microdomain is a Poisson spike train with an average frequency of (A) 2 Hz, (B) 10 Hz, (C) 5 Hz, (D) 7 Hz, (E) 3 Hz, (F) 9 Hz, (G) 8 HZ, (H) 4 Hz. Note that there is no noticeable phase locking of the individual Ca²⁺ oscillations.

Figure 18. Total Ca²⁺ oscillation and neural firing activity in AM-FM mode.

(A) Total Ca²⁺ oscillation and Ca²⁺ threshold (dashed line). (B) f function. (C) Neural firing activity of N1. (D) Neural firing activity of N2. Note how total Ca²⁺ is much more erratic. As a result the coordinated bursting of N1 and N2 is less frequent since the total level of Ca²⁺ crosses the threshold from below less often. Furthermore, it can be seen that f is activated for a much greater period of time (e.g. between 28 s and 94 s) since the total level of Ca²⁺ does not cross the threshold from above.

Figure 19. Individual Ca²⁺ oscillations and IP₃ levels in AM mode.

(A–H) Individual Ca²⁺ oscillations (black), IP₃ transients (red) in each of the 8 microdomains associated with the synapses of N1 (A–D) and N2 (E–H). The input stimulus to each microdomain is a Poisson spike train with an average frequency of (A) 5 Hz (0 s–100 s), (B) 9 Hz (2 s–100 s), (C) 15 Hz (4 s–100 s), (D) 6 Hz (6 s–100 s), (E) 10 Hz (8 s–100 s), (F) 12 Hz (10 s–100 s), (G) 8 HZ (12 s–100 s), (H) 7 Hz (14 s–100 s). Note how the phase of the individual oscillations phase lock each microdomain Ca²⁺ oscillation.

Figure 20. Total Ca²⁺ oscillation and neural firing activity in the AM mode.

(A) Total Ca²⁺ oscillation and Ca²⁺ threshold (dashed line). (B) f function. (C) Neural firing activity of N1. (D) Neural firing activity of N2. Note how total Ca²⁺ is much more erratic up until ∼40 s. As a result, the coordinated bursting of N1 and N2 during this time does not have a constant period. After ∼40 s phase locking of the individual microdomains is achieved and the coordinated activity of N1 and N2 is more constant. Furthermore, the total Ca2+ oscillation once again becomes much more regular.

Figure 21. Individual Ca²⁺ oscillations and IP₃ levels in the AM-FM mode.

(A–H) Individual Ca²⁺ oscillations (black), IP₃ transients (red) in each of the 8 microdomains associated with the synapses of N1 (A–D) and N2 (E–H). The input stimulus to each microdomain is a Poisson spike train with an average frequency of (A) 2 Hz, (B) 10 Hz, (C) 5 Hz, (D) 7 Hz, (E) 3 Hz, (F) 9 Hz, (G) 8 HZ, (H) 4 Hz. Note there is no phase locking of the individual microdomain oscillations.

Figure 22. Total Ca²⁺ oscillation and neural firing activity in the AM-FM mode.

(A) Total Ca²⁺ oscillation and Ca²⁺ threshold (dashed line). (B) f function. (C) Neural firing activity of N1. (D) Neural firing activity of N2. Note how total Ca²⁺ is much more erratic and infrequently crosses the threshold from above and below. Although the f function is activated for much longer periods, negative feedback is still unable to cause phase locking. As a result the coordinated bursting activity of N1 and N2 is significantly reduced.