Exploring Retrograde Signaling via Astrocytes as a ...

Exploring Retrograde Signaling via Astrocytes as a Mechanism for Self Repair John J. Wade, Liam J. McDaid, Jim Harkin, Vincenzo Crunelli, and J. A. Scott Kelso

Abstract— This paper presents a model of self repair at the level of synapses where retrograde signaling via astrocytes increases the probability of neurotransmitter release at damaged or low transmission probability synapses. The model draws from existing work on bidirectional coupling between astrocytes and neurons and indirect retrograde signaling, where the messengers are endocannabinoids. Although our model is still at the embryo stage results presented are encouraging and highlight a new research direction on brain-like self repair.

I. INTRODUCTION Reliability has traditionally been a design challenge in mission critical electronic systems [1-3]. However this challenge is now migrating into everyday non-critical systems where engineers must aim to design reliable systems on unreliable fabrics [4]. Traditional approaches to fault tolerant computing incorporate redundancy/replication models [5-8], error correction techniques [9] and radiation hardening [3, 7]. However, such approaches only provide limited levels of reliability as inherent architectural constraints are placed on the number and type of faults that can be tolerated and the level of granularity with which repairs can be implemented. More recent approaches to improving system reliability have looked to nature for inspiration in exploiting self-x properties including self-diagnosis, self-repair and selforganization [4]. The reasonable success to date of these bioinspired ‘evolutionary’ approaches [4, 10] over conventional approaches underpins the belief that to fully realize fault tolerant and self-repairing capabilities, future systems will need to harness similar mechanisms that are found in nature. Existing bio-inspired approaches [11-12] have exploited the programmability of Field Programmable Gate-Arrays (FPGAs) to provide adaptive repair at finer-levels of granularity. However, the levels of granularity are still insufficient as FPGA building blocks are typically coarse. Manuscript received February 28th, 2011. This work was supported in part by the Intelligent Systems Research Centre under the Centre of Excellence in Intelligent Systems grant, funded by the Integrated Development Fund. J. A. S. Kelso is also supported by NIMH Grant 080838, NSF grant BCS0826897 and US ONR award N000140510117. J. J. Wade, L. J. McDaid, and J. Harkin are with the Intelligent Systems Research Center, University of Ulster, School of Computing and Intelligent Systems, Derry, Northern Ireland BT48 7JL, U.K. (email: [email protected]; [email protected]; [email protected] V. Crunelli is with the Neuroscience Division, University of Cardiff, Cardiff School of Biosciences, Life Sciences Building, Museum Avenue, Cardiff, CF10 3AX, U.K. (email: [email protected]) J. A. S. Kelso is with the Intelligent Systems Research Centre and also the Center for Complex Systems & Brain Sciences, Florida Atlantic University, Boca Raton, Florida, USA. (email: [email protected])

Furthermore a central controller is used to make repair decisions, similar to more traditional approaches, which renders the entire repair process ineffective if it develops a fault. Moreover, as industry scales to Tera-Device Computing the number and stochastic nature of faults will become more significant and extremely challenging to mitigate [10]. Therefore, there is a need to explore beyond existing approaches to assist in developing highly adaptive, distributed computing systems that can, at fine levels of granularity, fault detect, diagnose and self-repair autonomously, without the constraint of a central fault detect/repair unit [9]. A novel approach to fault tolerant computing, which goes beyond existing capabilities, is to realize computations using neural networks, instead of traditional von Neumann computing architectures, exploiting the biological adaptive/repair mechanisms of the brain [13-15]. Neural networks are a fine-grained distributed computing architecture that captures the high levels of parallel processing in the brain. The fine-grained parallelism provides the framework that enables fault tolerance to be realized at very low levels of granularity; i.e. computations are mapped across many neuron clusters permitting a “scattering” of faults without a significant level of computing degradation. However, the high level of parallelism is not the only contributor to this phenomenon, as the brain uses key repair mechanisms to continually adapt to conditions via rewiring pathways to cope with decaying or damaged neurons [16]. The key challenge is, then, to understand the mechanisms that underpin the brain’s distributed and finegrained repair capability. To this end, we propose in this paper a model for self repair based on the interactions between astrocytes and neurons. We believe that our model will have significant impact across several research domains. Firstly, a model of the dynamic and coordinated interplay between distributed astrocytes and neurons will seed a completely new approach to fault tolerant computing thus providing a blue print for a radically advanced roadmap to self-repairing architectures. Secondly, from the neuroscience perspective, a model of bidirectional signaling between astrocytes and neurons will have significant implications where localized and global signaling via astrocytes, as well as their intrinsic plasticity, will provide important insight into how the brain adapts and repairs itself after injury or disease. Section II provides a review of the bidirectional communication properties between astrocytes and neurons. Section III presents a model of endocannabinoid self repair based on astrocyte-neuron interactions while section IV

details results for the model. Finally section V draws conclusions to the paper and gives direction on future work. II. BACKGROUND: ASTROCYTE-NEURON COMMUNICATION Traditionally, communication, information transfer and plasticity within the brain have been the sole province of the chemical synapses made by pre- and post-synaptic neurons. However, current research has challenged this view of synaptic physiology. Recent research now shows that ~50% of synapses are composed of an intimate connection between astrocytes and neurons that facilitates chemical communication: a synapse actually exchanges signals at three terminals, hence the name tripartite synapse [17]. For many years, astrocytes, a type of glial cell found in the central and peripheral nervous system, have been thought to provide structural support and vital chemicals to neurons, and to maintain physiological concentrations of ions and transmitters in the extracellular space [18-20]. In recent years, however, several new discoveries have revealed that astrocytes can encapsulate ~105 synapses and can connect to multiple neighboring neurons [21-22]. Although astrocytes cannot elicit propagating action potentials (APs) like neurons do, their “unit of excitation” is the transient increase in intracellular calcium (Ca2+) levels that is elicited by various neurotransmitters (e.g. glutamate, ATP, GABA, etc.) following binding to their respective receptors on the astrocytic membrane. These astrocytic Ca2+ transients in turn lead to astrocytic release of transmitters (often referred to as “gliotransmitters”) and to propagating Ca2+ waves [23-24]. Although the propagation of intracellular Ca2+ is not fully understood the process is believed to be facilitated by propagating signaling proteins between microdomain clusters of inosotil 1, 4, 5-trisphosphate Receptors (IP3Rs) [25-26]. Astrocytes also communicate in a feedback mode with neurons. This bidirectional communication between astrocytes and neurons results in various forms of synaptic modulation. Astrocytes have also recently been found to possess binding sites for endocannabinoids, a type of retrograde messenger released post-synaptically during neuronal depolarization [27]. Similar to neurotransmitter uptake, this leads to the oscillation of Ca2+ within the astrocyte and the release of glutamate. This signaling pathway acts to modulate the transmission probability of the synapse and is a potential candidate for self repair of damaged or low probability synapses [28]. III. ENDOCANNABINOID MEDIATED SELF REPAIR Upon the arrival of an Action Potential (AP) at the presynaptic axon, neurotransmitter (glutamate) is released across the cleft and binds to receptors on the post-synaptic dendrite causing a depolarization of the post-synaptic neuron. When the post-synaptic neuron is sufficiently depolarized (e.g. emits an output spike) voltage gated channels on the dendrite allow the influx of Ca2+ into the dendrite causing endocannabinoids to be synthesized and subsequently released from the dendrite. However, the exact

release machinery related to this process is not fully understood [27]. Endocannabinoids are a type of retrograde messenger which travel back from the post-synaptic terminal to the pre-synaptic terminal. The release of 2-arachidonyl glycerol (2-AG), a type of endocannabinoid, is known to feed back to the pre-synaptic terminal in two ways: 1) Directly: 2-AG binds directly to type 1 Cannabinoid Receptors (CB1Rs) on the pre-synaptic terminal. This results in a decrease in transmission probability (PR) and is termed Depolarization-induced Suppression of Excitation (DSE) [27]. 2) Indirectly: 2-AG binds to CB1Rs on an astrocyte which enwraps the synapse increasing IP3 levels within the astrocyte and triggering the intracellular release of Ca2+. This results in the astrocytic release of glutamate which binds to pre-synaptic group I mGluRs. This signaling results in an increase of synaptic transmission probability termed e-SP [28]. Experimental evidence shows that local synapses (i.e. synapses where post-synaptic firing results in direct and indirect signaling) exhibit DSE and PR is reduced by ~50%. This is thought to be as a result of the direct signaling pathway overpowering the indirect pathway. The direct signaling pathway is very local since 2-AG can only travel ~20nM within the extracellular fluid and therefore binds only with a few neighboring synapses. The indirect signaling pathway is however far reaching and can affect distant synapses [28]. Since astrocytes can enwrap ~105 synapses and contact ~6 neurons [22], the indirect signaling pathway has the potential to reach many synapses via the astrocyte. Distal silent synapses expressing indirect signaling via the astrocyte only, exhibit e-SP where PR increases by ~200% [28]. The present work explores the indirect feedback of 2AG via astrocytes which results in the increase of PR in neighboring synapses and is the repair mechanism proposed and modeled here. Given these known properties of endocannabinoids on the modulation of synaptic transmission probability, we speculate here that the indirect signaling pathway is the catalyst for self repair of damaged or low probability synapses. For instance, consider the case where a synapse is damaged with a low PR insufficient to cause post-synaptic activity. Because this neuron is not emitting 2-AG its associated synapses will experience an increase in PR due to the release of 2-AG from neighboring neurons. This messenger causes the release of glutamate from the astrocyte cell activating type I mGluRs in the presynaptic terminal. The proposed self repairing model is shown in the next section and builds on two biophysically motivated models which describe the interactions between astrocytes and neurons in a tripartite synapse: namely the gatekeeper model [29] and the Nadkarni and Jung model [30-31]. Both of these models use Li and Rinzel calcium dynamics [32] to describe the evolution of synapse driven Ca2+ within the astrocyte; Ca2+ regulates synapse transmission via the release of glutamate which binds to pre-synaptic receptors.

A. Astrocyte – Neuron Endocannabinoid Signaling Both the gatekeeper [29] and Nadkarni and Jung [30-31] models describe the interaction of astrocytes and neurons via the tripartite synapse. In a tripartite synapse an astrocyte process connects with the axon and dendrite of the pre- and post-synaptic neurons and is sensitive to the neurotransmitters within the extracellular fluid in the synaptic cleft [17]. However, in the current work we only model the astrocytes sensitivity to 2-AG instead of neurotransmitter. Fig. 1 describes a tripartite synapse with 2AG signaling. ER

Axon

Ca2+ Glu

3

Glu

(1)

where AG is the quantity of 2-AG, τAG is the decay rate of 2AG (=10s), rAG is the 2-AG production rate (= 0.9µM/s) and tsp is the time of the post-synaptic spike. Note we set τAG = 10s as the life time of 2-AG is unclear but the effects of e-SP are known to have a rise time ~100s and a decay time ~200s [28], therefore we assume that the lifetime of 2-AG is proportionally large. B. Astrocyte Calcium Dynamics In the presented model, 2-AG binds to CB1Rs on the astrocyte process and the generation of IP3 is achieved in a similar manner to the gatekeeper model [29] This process is assumed to be dependent on the amount of 2-AG released. The generation of IP3is given by: d [IP3 ] IP3* − IP3 = + rip 3 AG τ ip 3 dt

IP

2-AG

dAG − AG = + rAGδ (t − t sp ) dt τ AG

2-AG Astrocyte Process

Dendrite

Fig. 1. A Tripartite Synapse; axon and dendrite are involved with the release and uptake of neurotransmitter.

When neurotransmitter, e.g. glutamate, is released into the synaptic cleft and the post-synaptic neuron is sufficiently depolarized, 2-AG is released from the dendrite and binds to CB1Rs on the astrocyte process. This in turn initiates the creation and release of IP3 into the cytoplasm of the astrocyte which subsequently binds to IP3 receptors (IP3Rs) on the Endoplasmic Reticulum (ER); the ER is a long network of tubes and vesicles used to store calcium within the cell [20]. The binding of IP3 with IP3Rs opens channels that allow the release of Ca2+ from the ER in to the cytoplasm (Ca2+ puff). While individual Ca2+ puffs are incapable of propagating intracellularly, several puffs can raise Ca2+ levels in the cytoplasm beyond a threshold and an oscillating Calcium Induced Calcium Release (CICR) propagation can be observed [33]; the threshold is believed to be of the order 0.2-0.4 µM [34]. The increase in cytosolic Ca2+ then causes the release of gliotransmitter, back into the synaptic cleft which binds to presynaptic group I mGluRs, i.e. indirect signaling. The 2-AG also binds directly (direct signaling) to the presynaptic CB1Rs which causes a decrease in PR. In this work we only consider the indirect long range signaling pathway. To model 2-AG release we assume each time a post synaptic neuron fires, a puff of 2-AG is released into the cleft and can be described as follows:

(2)

where IP3 is the amount within the cytoplasm. rip3 is the production rate of IP3 and is set at 0.5µM/s, IP3* is the baseline of IP3 within the cytoplasm when the cell is in a steady state and receiving no input, rip3 is the rate at which IP3 is produced, and τip3 is the IP3 decay rate. Calcium is stored within the ER by pumping calcium out of the cytoplasm into the ER, and is released by leakage through the ER membrane or by the opening of calcium channels by IP3Rs. To describe the calcium dynamics within an astrocyte, the gatekeeper [29] and the Nadkarni and Jung models [30-31] employed the Li-Rinzel model [32] which describes the pump, leak and IP3 dependent regulation of Ca2+. Our model also uses the Li and Rinzel model to emulate the astrocyte Ca2+ dynamics and is described using the following equations:

[

]

d Ca 2 + = − J chan − J pump − J leak dt dq = α q (1 − q ) − β q q dt

(3) (4)

where Jchan is the IP3 dependent Ca2+ release, Jpump is the amount of Ca2+ pumped from the cytoplasm into the ER, Jleak is the Ca2+ which leaks out of the ER and q is considered to be the fraction of activated IP3Rs. The parameters α q and

β q are given by: α q = a2 d 2

[IP3 ] + d1 [IP3 ] + d 3

(5)

and

[

β q = a2 Ca 2 +

]

(6)

The description of the three channels is given by:

([

] [

J chan = c1v1m∞3 n∞3 q 3 Ca 2 + − Ca 2 +

] ) ER

(7)

J pump =

[

v3 Ca 2 +

[

]

2

k32 + Ca 2 +

([

(8)

]

2

] [

J leak = c1v2 Ca 2 + − Ca 2 +

] ) ER

(9)

where m∞ is the IICR (IP3 Induced Calcium Release) channel given by:

[IP3 ] m∞ = [IP3 ] + d1

(10)

and n∞ is the CICR channel given by:

[Ca ] [Ca ]+ d

dependent on the quantity of glutamate released by the astrocyte. Note that all parameters and initial variable values used throughout this paper can be found in Tables 1-2 of the Appendix. IV. RESULTS We now present results of simulations which show the dynamics of our model and how self repair can occur at distal synapses. Consider the case where neuron N1 is firing at some unspecified rate. The astrocyte receives a 2-AG signal causing the release of glutamate which acts on receptors on the presynaptic terminal of N2.

2+

n∞ =

(11)

2+

5

Therefore, the release of Ca2+ from the ER is both dependent on the levels of IP3 and Ca2+. Once the change in Ca2+ has been calculated, Ca2+ concentration in the ER ([Ca2+]ER) can be calculated as:

ER

=

[

c0 − Ca 2 + c1

]

(12) Fig. 2. SNN fragment illustrating endocannabinoid mediated self repair.

where co and c1 are constants (see Table 1). C. Astrocyte feedback The intracellular astrocytic calcium dynamics is then used to regulate the release of glutamate from the astrocyte. To model this release, we assume when Ca2+ crosses the CICR threshold from below that a puff of glutamate targeting group I mGluRs is released and is given by:

dGlu −Glu = + rGlu δ (t − t Ca ) τ Glu dt

0.2

(13) 0.15

deSP = −eSP + meSP Glu (t ) dt

0 0

50

100

150 Time ( s )

200

250

300

Fig. 3. 2-AG Kinetics; 2-AG is released as a result of the post-synaptic Stimuli from N1. Note how 2-AG builds until it reaches a plateau at ~50s.

The resulting IP3 and Ca2+ dynamics can be seen in Fig. 4. 0.8

IP3 / Ca

To model the effects of e-SP we use the following:

0.1 0.05

2+

where Glu is the quantity of glutamate, τGlu is the decay rate of glutamate (=100ms), rGlu is the glutamate production rate (= 10µM/s) and tCa is the time of the Ca2+ threshold crossing. It is believed that Ca2+ oscillations can be initiated within discrete microdomains and can be localized or propagated intracellularly by activating neighboring microdomains of storage [25-26, 38-36]. Therefore, the level of Ca2+ within the cell will differ depending on spatial location. However, to maintain simplicity in our model we assume that the instantaneous level of Ca2+ remains the same everywhere; therefore the release of glutamate is also assumed to be instantaneous.

τ eSP

Note that the post-synaptic firing process is not modeled explicitly as we assume that the synapse is in a state of equilibrium between DSE and e-SP and is producing postsynaptic spiking activity modeled simply as a binary Poisson spike train. Therefore, S1 is stimulated for a burst duration of 100s with a 15Hz Poisson encoded spike train from N1. Fig. 3 shows the evolution of 2-AG as a result of the postsynaptic stimulation.

2-AG ( µM )

2+

( µM )

[Ca ]

IP3

0.6

Ca2+

Ca2+ Threshold

0.4 0.2

(14)

where τeSP is the decay rate of e-SP (=40s) and meSP is a weighting constant (=2x105) used to control the height of eSP. From equation (14) it is clear that the level of e-SP is

0 0

50

100

150 Time ( s )

200

250

300

Fig. 4. Astrocyte IP3 and Ca2+ Dynamics; when Ca2+ crosses the threshold from below glutamate will be released from the astrocyte.

Note that when Ca2+ crosses the threshold from below the astrocyte releases a puff of glutamate. This is described in Fig. 5. 0.01

Glu ( µM )

0.008 0.006 0.004 0.002 0 0

50

100

150 Time ( s )

200

250

300

Fig. 5. Glutamate released by the astrocyte as a result of intracellular Ca2+ levels crossing the threshold from below.

Finally, the astrocytic glutamate modulates the synaptic transmission probability according to equation (14) as shown in Fig. 6. 200

e-SP ( % )

150

APPENDIX TABLE 1. ASTROCYTE PARAMETERS

100 50 0 0

Therefore, our hypothesis is that the emergence of low transmission probability synapses, which result in silent neurons, is how a ‘fault’ is detected and the enhancement of the transmission probability of this synapse by indirect retrograde feedback is the repair mechanism. Although many details remain to be worked out, the model does enhance our understanding of the complex nature of astrocyte-neuron communication. However, current research is developing the endocannibinoid model to include DSE dynamics and explore the interactions of both direct and indirect signaling pathways. We view models of this complexity as essential if we are to capture the complex interplay between networks of astrocytes and neurons. Furthermore, modeling the interaction between these cells at network level will lead to a truly brain-inspired paradigm for fault tolerant computing [40] and beyond with self-repairing hardware architectures. In addition, better models of the repair process at the cellular level will provide important insight into how the brain adapts and repairs itself after injury or disease.

50

100

150 Time ( s )

200

250

300

Fig. 6. e-SP Kinetics; synaptic modulation now takes place according to the e-SP curve.

Fig. 6 clearly shows that as the astrocyte releases 2-AG driven glutamate, the firing probability of the synapse will be increased by ~200% in agreement with published work [28]. Therefore, in the case where a damaged or low probability synapse is unable to cause postsynaptic firing, non local driven increase of the firing probability will take place via the astrocyte-neuron endocannabinoid signaling. This model of self repair could easily be incorporated into various synapse models [37-39] to implement fault diagnosis and repair at the network level. V. CONCLUSION This paper draws on published work to produce a model of the coupling between astrocytes and neurons, and in doing so, has provided strong evidence to support the hypothesis that astrocyte networks provide much more than structural support to neural networks. Indeed astrocytes are viewed as regulators of neural circuitry through coordination of transmission at the synapse. Moreover, it is also believed that retrograde messengers induced in the post-synaptic neuron can be fed back either directly or via astrocyte cells to receptors on the pre-synaptic neuron [28]. The model presented in this paper, captures the endocannabinoid interaction between astrocytes and neurons demonstrating that positive feedback to non local synapses is possible, via astrocytes, and as a consequence of this feedback the transmission probability in remote synapses is enhanced.

Astrocyte Parameter

Value

IP*3 rIP3 rAG rGlu τAG τIP3 τCa τGlu τeSP v1 v2 v3 c0 c1 d1 d2 d3 d5 meSP Ca2+ Threshold

0.16 µM 0.5 µM s-1 0.9 µM s-1 10 µM s-1 10 s 7s 1s 100 ms 40 s 6 s-1 0.11 s-1 0.9 µM s-1 2 µM 0.185 0.13 µM 1.049 µM 0.9434 µM 0.08234 µM 2x105 0.3 µM

TABLE 2. ASTROCYTE INITIAL VARIABLES

Astrocyte Variable

Initial Value

Ca2+ q chan Jpump Jleak m∞ n∞ αq βq Ca2+ER AG Glu eSP IP3

0.0722 µM 0.7924 0 0 0 0 0 0 0 (c0/Ca2+)/c1 µM 0 0 0 0.16 µM

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