Neurophysiological Analysis of Schizophrenia

Based On Dysfunction of the Glutamatergic

System Using a Tripartite Synapse Model

Ali Mahdavi

School of ECE, College of Engineering

University of Tehran

Tehran, Iran

ali.mahdavi.o@ut.ac.ir

Fariba Bahrami

CIPCE, School of ECE, College of Engineering

University of Tehran

Tehran, Iran

fbahrami@ut.ac.ir

Mahyar Janahmadi

Shahid Beheshti University of Medical Sciences

Tehran, Iran

Janahmadi@sbmu.ac.ir

Abstract—Schizophrenia is a severe chronic psychiatric

disorder and its pathology is still not completely known.

However, up to now several different theories have been

proposed to describe the pathophysiology of schizophrenia.

Hypofunction of NMDA receptors (NMDAR) and inactivated

astrocytes are among important glutamatergic theories

explaining the pathophysiology of schizophrenia. On the other

hand, it has been suggested that pharmacological manipulation

of presynaptic metabotropic glutamate receptors (mGluRs)

may help to treat and improve some symptoms of

schizophrenia. In this paper we propose a mathematical model

at the synaptic level to investigate glutamatergic hypothesis of

schizophrenia. In the proposed model, we described

mathematically a single tripartite synapse that is consisted of

one presynaptic and one postsynaptic neuron and a glial

component that is the astrocyte. The proposed model describes

different details of a tripartite synapse during glutamate

release. To the best of our knowledge, at the moment this is the

most extended mathematical model developed to describe the

details of a tripartite synapse to this extend. Simulation results

of the proposed model indicate that hypofunction of NMDAR

might be caused by excessive amount of glutamate in the

synaptic cleft. The increased amount of glutamate, in final

analysis, can be caused by inactive astrocyte. The increased

amount of glutamate in synaptic cleft may cause serious

disturbances in NMDAR current and electrophysiological

behavior of the postsynaptic neuron. Given these results, we

suggest that manipulation of glutamate receptors on astrocyte

may be a suitable strategy in the treatment of schizophrenia. Of

course, other approaches that help to improve the function of

glutamate transmission or use agonists of mGluRs or NMDARs

might be also useful. Our simulation results also suggest that

the mentioned theories about pathophysiology of schizophrenia

are interrelated and the increased rate of clearance of

glutamate from the synaptic cleft can partly compensate for

disorders caused by the impaired astrocyte.

Keywords-Schizophrenia, astrocytes, glutamate, tripartite

synapse, mathematical model, NMDA receptors

I. INTRODUCTION

A. Schizophrenia and its symptoms

Schizophrenia is a severe mental disorder and a chronic

psychiatric illness. There are three main symptoms for

schizophrenia. These symptoms include positive, negative,

and cognitive. Positive symptoms include delusions,

hallucinations, agitation and paranoia. Negative symptoms

are characterized by the absence of behaviors that are

normally present, including flat affect, poverty of speech and

social withdrawal. Cognitive deficits are such as

disorganized thoughts, conceptual disorganization and

memory problems. So we can say that perception,

conception, attention, motion, emotion and cognition are

impaired in schizophrenia [1], [2].

Several pharmaceutical and experimental evidences reveal

manipulation of dopamine and glutamate receptors can lead

to emerging disorders and symptoms similar to schizophrenia

[1], [3], [4], [5], [6], [7].

There are several qualitative models (theories) describing

pathophysiological effects of schizophrenia [3], [6], [7].

However, to the best of our knowledge, up to today no

mathematical model at the synaptic level has been developed

which is able to describe different pathophysiological effects

of schizophrenia.

Therefore, before describing our proposed model, we

explain theories and physiological models that we used to

develop this mathematical model.

B. NMDAR hypofunction theory

The first treatments for schizophrenia were found by

mediating dopamine receptors. Thereby, Dopamine system

in schizophrenia was proposed as a big theory [3].

However, weaknesses of the dopaminergic model became

gradually apparent, because this model had different

limitations and problems. For example, dopaminergic model

was only able to explain the positive symptoms, and was

unable to explain the negative and cognitive symptoms [1],

[4].

During the 90s, observations obtained from the usage of

phencyclidine (PCP) led to another theory called later as the

glutamatergic theory [4], [5]. According to this theory and

psychopharmacological and postmortem findings, there is a

dysfunction in the glutamate neurotransmission, especially

activity of NMDARs. Since, blocking NMDA receptors

reproduce key symptoms of schizophrenia, thus it appears

Proceedings of 20th Iranian Conference on Biomedical Engineering (ICBME 2013), University of Tehran, Tehran, Iran,December 18-20, 2013

978-1-4799-3232-0/13/$31.00 ©2013 IEEE 183

that hypofunction of NMDARs play a critical role in

emerging the symptoms of schizophrenia and thereby, in the

pathophysiology of schizophrenia. Abnormal glutamate

neurotransmission may be caused by dysregulation or

dysfunction of NMDA receptors [1], [5], [6].

These findings led to the emergence of glutamatergic

model that supports a major role for the impaired glutamate

neurotransmission and dysfunction of glutamate receptors in

the pathophysiology of schizophrenia [1], [6], [7].

Pharmacological manipulation of glycine site of NMDA

receptors by agonists and coagonists can improve number of

symptoms of schizophrenia [8].

Since the use of NMDAR antagonists lead to appearance of

symptoms of schizophrenia and injection of NMDAR co-

agonists such as D-Serine lead to potentiation of NMDAR

and thus improving some of symptoms, these findings

suggest that focus on the NMDA receptors may be a

treatment strategy for improving the symptoms of

schizophrenia [8].

C. Pathologic astrocyte in schizophrenia

Glial cells are involved in the regulation and the

modulation of synaptic neurotransmission and neuronal

activity [9].A tripartite synapse consists of the presynaptic

and postsynaptic neuron and the glial component (astrocyte).

A number of findings suggest that abnormalities of

tripartite synapse can lead to the mental disorders such as

schizophrenia and bipolar disorders[10], [11].

Gliotransmitters such as glutamate, D-Serine and ATP are

chemical materials that are released by astrocytes.

Glitransmitters can activate the glutamate receptors of

neurons.The released Glutamate by astrocyte can activate

glutamate receptors particularly metabotropic glutamate

receptors (mGluRs) and the released D-Serine from astrocyte

can help activating the glutamate receptors specially

NMDARs. So astrocyte regulates the synaptic activity and

synchronizes the neurons by release of glitransmitters [9],

[12], [13].

Figure 1. A model inspired by [9] and [10] for a tripartite synapse. pr.R:

Presynaptic Receptor, gl.R: Glutamate Receptor, NT:

Neurotransmitter, po.R: Postsynaptic Receptor.

In tripartite synapse of schizophrenia there are Non-

functional receptors on the astrocyte. So that

neurotransmitters cannot bind to these receptors (depicted in

Fig. 2). Since astrocyte is not able to the production and

release of gliotransmitters, therefore there is no negative

feedback to the presynaptic receptors (see Fig. 2). Fig. 2 is

inspired from [10] and [11].

Shortage in releasing glutamate from astrocyte and

therefore the loss of feedback to the presynaptic

metabotropic glutamate receptors leads to excessive and

unconstrained release of glutamate from presynaptic terminal

to synaptic space. This disorder leads to dysfunction of

glutamate receptors, particularly NMDARs on the

postsynaptic terminal. This severe disturbance in the

tripartite synapse leads to an unconstrained

neurotransmission and appearance of symptoms of

schizophrenia [10], [11].

Figure 2. Proposed model for an impaired tripartite synapse corresponding

to pathologies in schizophrenia. gl.Rs are inactive, therefore, GTs

are not produced by astrocyte and there is no negative feedback. This disorder leads to unconstrained neurotransmission. gl.R:

Glutamate Receptor, NT: Neurotransmitter, pr.R: Presynaptic

Receptor, po.R: Postsynaptic Receptor.

In the next section is shown that using mGluRs agonists

can control and regulate release of presynaptic glutamate and

improve these disorders.

D. Treatment with metabotropic glutamate receptors

Preclinical and pharmacological findings suggest that

agonists of mGluRs improve some symptoms of

schizophrenia particularly cognitive deficits and almost

compensate effects of NMDA antagonists [15].

Figure 3. Two types of mGluRs are effective in NMDA receptor functions. The mGlu2/3 receptor regulates and inhibits the

release of presynaptic glutamate. The mGlu5 receptor modulates

the function of NMDARs. The mGluRs are important in treating schizophrenia.

Proceedings of 20th Iranian Conference on Biomedical Engineering (ICBME 2013), University of Tehran, Tehran, Iran,December 18-20, 2013

978-1-4799-3232-0/13/$31.00 ©2013 IEEE 184

Fig. 3 is inspired by [15], [16]. This figure shows that the

activated mGluRs on presynaptic neuron particularly

mGluR2/3 inhibit the release of glutamate. These receptors

can active by astrocytic glutamate [14]. Therefore mGluRs

on presynapse can regulate the amount and probability of

release of glutamate. Since in the tripartite synapse of

schizophrenia there is no negative feedback from astrocyte,

so these receptors aren’t activated enough. These findings would suggest that manipulation and

activation of mGluRs by their agonists is a strong treatment

strategy for the negative symptoms and cognitive

impairments of schizophrenia [16], [17]. The mGlu5 is

located on postsynaptic neuron and mGluR2/3 receptor is

located on the presynaptic neuron. These receptors are two

targets for improving some symptoms of schizophrenia,

which can regulate and modulate the glutamate

neurotransmission. The activation of mGluRs may be a

strong strategy for improving cognitive deficits [16]. In this

paper, we consider only mGluRs located on presynaptic

neuron.

In this paper we provide a mathematical framework for

the synaptic interactions between neurons and pathologic

astrocyte according to tripartite synapse of schizophrenia.

Model shows pathologic astrocyte may cause defects in the

function of glutamate receptors on presynaptic and

postsynaptic neuron and so impaired the synaptic

transmission and postsynaptic events.

II. METHOD

A. A model to describe a healthy tripartite synapse

Although many models have been proposed to tripartite

synapse by different persons, but these models are not

suitable for modeling of pathophysiology of schizophrenia.

On the other hand, we need a tripartite synapse model that is

applicable for using in schizophrenia model, therefore in this

paper, we present a mathematical model based on a

biological model of pathologic astrocyte in a tripartite

synapse of schizophrenia. For mathematical modeling of

different parts of tripartite synapse, we used distinct existing

mathematical models for each part. The following steps have

been followed in simulation of this model (see Fig. 4).

Figure 4. Different steps of information flow from presynaptic terminal to

postsynaptic neuron and modulatory effect of the astrocyte. Solid line shows the effect of presynaptic neuron, and solid dashed

lines show the effect of astrocyte.

Fig. 4 is inspired by [18], [22], [23]. Here, we explain

steps presented in Fig. 4: (1) Presynaptic action potential

train is generated using the proposed model by Jakub

Nowacki et al [19]. (2) Ca2+

concentration elevation in the

presynaptic neuron. (3) Glutamate release in the synaptic

cleft. (4a) Glutamate modulated enhancement of astrocytic

Ca2+

. (4b) Glutamate mediated excitatory postsynaptic

potential. (5) Astrocytic glutamate elevation as a

consequence of (4a) [18]. Processes modeled in our tripartite

synapse model are presented in TABLE I. and this tripartite

synapse is located in the hippocampus region and all model

parameters are adjusted with this region.

TABLE I. LIST OF REFERENCE USED IN DEVELOPMENT OF OUR PROPOSED MODEL

Process Reference model

Presynaptic action potential [19]

Presynaptic Ca2+

dynamics [20]

Glutamate release dynamics

in presynaptic terminal [21],[22]

Glutamate dynamics in

synaptic cleft [23],[18]

Astrocyte Ca2+

dynamics [23]

Gliotransmitter release

dynamics in astrocyte [21], [25]

Dynamics of astrocytic

glutamate [18]

Gating and current of receptors:

AMPAR, NMDAR [18], [24], [26]

Postsynaptic membrane

potential [27]

Because we would like to see the effects of astrocyte on

the NMDAR current, we added model of NMDAR current to

tripartite synapse model. Model of NMDAR current has

specific features. In our model, the synaptic glutamate and

conductance of NMDAR channel are not constant and they

are variable and have dynamics. Dynamics of conductance of

NMDAR channel and synaptic glutamate are proposed by

Moradi et al [26] and Tewari et al [18], respectively.

B. A model of pathologic tripartite synapse

First, presynaptic neuron fire, then glutamate release from

the vesicles. Of course release of glutamate is a stochastic

process and after the firing of neuron, it is likely to be

released or not. The released glutamate is transported from

presynaptic terminal to postsynaptic membrane or astrocyte.

These glutamates bind to mGluRs on the astrocyte. Then

mGluRs trigger production of the second messenger IP3 in

the astrocyte. Production IP3 leads to release of Ca2+

from

the endoplasmic reticulum. Then when Ca2+

concentration

was higher than a certain threshold, glutamate release from

astrocyte.The released Glutamate by astrocyte can bind to

presynaptic mGluRs. Then these activated mGluRs inhibit

Proceedings of 20th Iranian Conference on Biomedical Engineering (ICBME 2013), University of Tehran, Tehran, Iran,December 18-20, 2013

978-1-4799-3232-0/13/$31.00 ©2013 IEEE 185

the release of glutamate from the presynaptic neuron [18],

[22].

As mentioned in the previous section, one of important

theories in pathophysiology of schizophrenia is impairments

in astrocytes. According to this theory, the mGluRs on the

astrocyte are inactive and cannot generate the second

messenger IP3. This dysfunction leads to inability of

astrocytes to produce and release of gliotransmitters,

especially glutamate. Thus, in our model, if we want to

simulate a pathologic tripartite synapse, maximal production

rate of IP3 by binding of glutamate to mGluRs on astrocyte

( in equation (1) should be equal to zero.

(

)

(1)

Here, is astrocytic IP3 and is synaptic glutamate

concentration. Descriptions and values of parameters of (1)

are given in [18], [23]. With parameter equal to zero, we

could simulate pathologic astrocyte according to

schizophrenia. Of course we have reduced the value of by

half, too. Because is maximal rate of IP3 production by

PLCδ [18]. The results are presented in the next section.

The model was implemented in MATLAB 2012a.

Forward Euler method with a fixed time step of 0.05ms was

used for implementing ordinary differential equations.

III. RESULTS

In this section, we present our results for models of

healthy and pathologic tripartite synapse related to

schizophrenia .Then we will analyze the model and compare

the results with other works. The NMDA receptors are very

important in analyzing pathophysiology of schizophrenia.

For this reason, we modeled NMDAR current with specific

features which described in the previous section. For

modeling of NMDAR current, we used the overall structure

of the model of Destexhe et al [24].NMDAR current in our

model conforms to previous models. Fig 5 shows NMDAR

current in our model. To model dysfunction of NMDA

receptors, it is essential that glutamate and conductance of

NMDAR channel be variable not constant, because we want

to observe effects of changes in glutamate and abnormal

glutamate neurotransmission on NMDAR current. For this

reason, we have considered the dynamics of the glutamate

and conductance of NMDAR current.

Figure 5. a. NMDAR current for 60 ms in voltage clamp state

(Postsynaptic potential is 40 mv). NMDA receptor is activated

when presynaptic glutamate is released, b. A spike of NMDAR current in voltage 40 mv for validating the proposed model, c and

d. NMDAR current and voltage of the postsynaptic neuron when

the postsynaptic neuron is depolarized by released neurotransmitters of presynaptic neuron.

By comparing the results of Fig.5 with existing results in

[24], [26] and [28] it could be concluded that our NMDAR

model is valid.

Figure 6. Important variables of a tripartite synapse in the proposed model. A. healthy tripartite synapse, B. Pathologic tripartite synapse.

Fig. 6 shows the important variables of the tripartite

synapse in the proposed model. For simulation of

schizophrenic synapse, we have impaired the astrocyte. This

impairment is described in the previous section. Thus

glutamate does not release from astrocyte (see Fig. 6, B).

This dysfunction led to the loss of negative feedback from

astrocyte to presynaptic mGlu receptors and thereby an

increase in synaptic glutamate. Increasing the glutamate

concentration in the synaptic cleft leads to abnormal

neurotransmission and then dysfunction of postsynaptic

receptors particularly NMDARs.

0 1 2 3 4 5 6

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Proceedings of 20th Iranian Conference on Biomedical Engineering (ICBME 2013), University of Tehran, Tehran, Iran,December 18-20, 2013

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Figure 7. NMDAR current, A. Healthy, B. Impaired.

Fig. 7 shows that increasing the glutamate in the synaptic

cleft leads to severe dysfunction of NMDAR current. In

compare with healthy current, amplitude and intensity

fluctuations are reduced. This result suggests an increase in

released glutamate from presynaptic terminal may leads to

hypofunction of NMDA receptors.

Our results show NMDAR current is effective on the

postsynaptic membrane potential. Healthy current create

bursting mode in the postsynaptic potential, but disrupted

NMDAR current cannot (see Fig. 8). So dysfunction of

NMDAR may change mode of membrane potential. Thus in

schizophrenia not only NMDAR current but also membrane

potential may be impaired.

.

Figure 8. A. Membrane potential of a healthy postsynaptic neuron, B.

Membrane potential of a pathologic postsynaptic neuron, C and D. Membrane potential of a healthy and pathologic postsynaptic

neuron from a closer view, respectively. In C we observe that the

neuron is in bursting mode, while in D there is no burst.

Since increased glutamate leads to the disrupted NMDAR

current, it seems decreasing the glutamate may be effective

for modifying the function of NMDAR. The mathematical

equation of glutamate concentration dynamics in the cleft is

as follow [18]:

(2)

Here and are the variables of (2). is the glutamate

concentration in the synaptic cleft, gives the effective

fraction of vesicles in the cleft, is the number of vesicles,

is glutamate concentration in per vesicle and is the rate

of glutamate clearance from synaptic cleft. Values of these

parameters are proposed in [18]. Glutamate clearance can be

done by neurons, astrocytes or enzymes [18]. We increased

the rate of glutamate clearance totwice. Fig. 9 shows

increase in is partly able to compensate impairments of

NMDAR current. By increasing this parameter, impaired

NMDAR current has almost returned to its original state.

With this change, Fluctuations in NMDAR current and

postsynaptic potential are somewhat close to the healthy

mode. Fig. 9 shows postsynaptic potential returns to burst

mode partly.

Figure 9. Increasing the rate of glutamate clearance, synaptic activity

returns almost to its healthy state.

The proposed model suggests that the three major theories

of schizophrenia are fully inter-related with each other. Our

results show if astrocyte cannot produce and release the

glutamate, then the negative feedback from astrocyte to

presynaptic neuron would be interrupted and mGluRs would

not be activated. The mGluRs regulate and inhibit the release

of glutamate from vesicles. Therefore if these receptors are

not activated enough, release of the glutamate will be

increased. Most pharmacological evidences state that using

agonists of presynaptic mGluRs particularly mGluR2/3

agonists for activation of these receptors can improve the

cognitive symptoms of schizophrenia and use of antagonists

of these receptors lead to emerging the symptoms of

schizophrenia [15], [16].

NMDAR hypofunction is an important theory for

describing pathophysiology of schizophrenia. Simulation

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Proceedings of 20th Iranian Conference on Biomedical Engineering (ICBME 2013), University of Tehran, Tehran, Iran,December 18-20, 2013

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results of the proposed model indicate that schizophrenia

might be caused by increased level of synaptic glutamate.

Increased level of glutamate is caused by inactive

presynaptic mGluRs. Presynaptic mGlu receptors are

inactivated due to lack of feedback from astrocyte, that is

because astrocyte is not capable to produce and to release the

necessary glutamate into the synapse. Incapability of the

astrocyte is due to impaired receptors which cannot trigger

intrinsic processes of astrocyte such as production of IP3 and

calcium oscillations. Based on these results, we suggest that

diminishing the defects of astrocyte may be a suitable

treatment approach for schizophrenia. Of course other

approaches that help to improve function of glutamate

transmission or using the agonists of mGluRs or NMDARs

may also be useful.

IV. CONCLUSIONS

Results of our schizophrenic model of tripartite synapse

propose that dysfunction of glutamate neurotransmission

leads to hypofunction of NMDAR receptors on the

postsynaptic neuron. Impaired glutamate neurotransmission

is due to shortly activated mGluRs on presynaptic neuron.

Since there is no negative feedback from the astrocyte to

presynaptic neuron, the release of glutamate is not regulated

and controlled. We proposed a mathematical framework for

tripartite synapse according to schizophrenia that the

mGluRs on astrocyte are impaired. Therefore synaptic

glutamate cannot bind to these receptors. Consequently,

astrocyte does not able to production and release of

gliotransmitters particularly glutamates. Thus, our results

suggest that there is a strong correlation between the three

major theories of schizophrenia that are explained in the

introduction section.

The analysis of our model may help to understand the

pathology of schizophrenia better and contribute to findnew

treatment approaches.

In this paper, we did not investigate the critical role of D-

Serine in pathophysiology of schizophrenia. This modulator

is a coagonist for NMDA receptors that release from

astrocytes [29]. In future, we are going to add the D-Serine

dynamics to our model.

REFERENCES

[1] S. Bickel and D. C. Javitt, “Neurophysiological and neurochemical animal models of schizophrenia: focus on glutamate,” Behavioural

brain research, vol. 204, no. 2, pp. 352–362, 2009.

[2] S. R. Kay, A. Flszbein, and L. A. Opfer, “The positive and negative syndrome scale (PANSS) for schizophrenia.,” Schizophrenia bulletin,

vol. 13, no. 2, p. 261, 1987.

[3] P. Seeman, “Dopamine receptors and the dopamine hypothesis of schizophrenia,” Synapse, vol. 1, no. 2, pp. 133–152, 1987.

[4] D. C. Javitt and S. R. Zukin, “Recent advances in the phencyclidine

model of schizophrenia,” Am J Psychiatry, vol. 148, no. 10, pp. 1301–1308, 1991.

[5] D. C. Javitt, “Negative schizophrenic symptomatology and the PCP

(phencyclidine) model of schizophrenia.,” The Hillside journal of clinical psychiatry, vol. 9, no. 1, p. 12, 1987.

[6] J. W. Olney, J. W. Newcomer, and N. B. Farber, “NMDA receptor

hypofunction model of schizophrenia,” Journal of psychiatric research, vol. 33, no. 6, pp. 523–533, 1999..

[7] J. T. Coyle, “The glutamatergic dysfunction hypothesis for

schizophrenia,” Harvard review of psychiatry, vol. 3, no. 5, pp. 241–253, 1996.

[8] J. T. Coyle and G. Tsai, “The NMDA receptor glycine modulatory

site: a therapeutic target for improving cognition and reducing

negative symptoms in schizophrenia,” Psychopharmacology, vol.

174, no. 1, pp. 32–38, 2004. [9] T. Fellin, O. Pascual, and P. G. Haydon, “Astrocytes coordinate

synaptic networks: balanced excitation and inhibition,” Physiology,

vol. 21, no. 3, pp. 208–215, 2006. [10] B. Mitterauer, “Nonfunctional glial proteins in tripartite synapses: a

pathophysiological model of schizophrenia,” The Neuroscientist, vol.

11, no. 3, pp. 192–198, 2005. [11] B. J. Mitterauer, “Possible role of glia in cognitive impairment in

schizophrenia,” CNS neuroscience & therapeutics, vol. 17, no. 5, pp.

333–344, 2011. [12] A. Araque, V. Parpura, R. P. Sanzgiri, and P. G. Haydon,

“Glutamate-dependent astrocyte modulation of synaptic transmission

between cultured hippocampal neurons,” European Journal of Neuroscience, vol. 10, no. 6, pp. 2129–2142, 1998.

[13] T. Fellin, O. Pascual, S. Gobbo, T. Pozzan, P. G. Haydon, and G.

Carmignoto, “Neuronal synchrony mediated by astrocytic glutamate through activation of extrasynaptic NMDA receptors,” Neuron, vol.

43, no. 5, pp. 729–743, 2004.

[14] B. J. Mitterauer and B. Kofler-Westergren, “Possible effects of synaptic imbalances on oligodendrocyte–axonic interactions in

schizophrenia: a hypothetical model,” Frontiers in Psychiatry, vol. 2,

2011. [15] B. Moghaddam and B. W. Adams, “Reversal of phencyclidine effects

by a group II metabotropic glutamate receptor agonist in rats,”

Science, vol. 281, no. 5381, pp. 1349–1352, 1998. [16] B. Moghaddam, “Targeting metabotropic glutamate receptors for

treatment of the cognitive symptoms of schizophrenia,” Psychopharmacology, vol. 174, no. 1, pp. 39–44, 2004.

[17] J. M. Wierońska and A. Pilc, “Metabotropic glutamate receptors in

the tripartite synapse as a target for new psychotropic drugs,” Neurochemistry International, vol. 55, no. 1–3, pp. 85–97,

2009.

[18] S. G. Tewari and K. K. Majumdar, “A mathematical model of the tripartite synapse: astrocyte-induced synaptic plasticity,” Journal of

biological physics, vol. 38, no. 3, pp. 465–496, 2012.

[19] J. Nowacki, H. M. Osinga, J. T. Brown, A. D. Randall, and K. Tsaneva-Atanasova, “A unified model of CA1/3 pyramidal cells: An

investigation into excitability,” Progress in biophysics and molecular

biology, vol. 105, no. 1, pp. 34–48, 2011. [20] J. W. Shuai and P. Jung, “Stochastic Properties of Ca2+ Release of

Inositol 1, 4, 5-Trisphosphate Receptor Clusters,” Biophysical

journal, vol. 83, no. 1, pp. 87–97, 2002. [21] M. V. Tsodyks and H. Markram, “The neural code between

neocortical pyramidal neurons depends on neurotransmitter release

probability,” Proceedings of the National Academy of Sciences, vol. 94, no. 2, pp. 719–723, 1997.

[22] S. Nadkarni, P. Jung, and H. Levine, “Astrocytes optimize the

synaptic transmission of information,” PLoS computational biology, vol. 4, no. 5, p. e1000088, 2008.

[23] M. De Pittà, M. Goldberg, V. Volman, H. Berry, and E. Ben-Jacob,

“Glutamate regulation of calcium and IP3 oscillating and pulsating dynamics in astrocytes,” J BiolPhys, vol. 35, no. 4, pp. 383–411,

2009.

[24] A. Destexhe, Z. F. Mainen and T. J. Sejnowski, “Kinetic models of synaptic transmission,” In: Koch, C., Segev, I. (eds.) Methods in

Neuronal Modeling, MIT Press, Cambridge, pp. 1–25, 1998.

[25] V. Parpura and P. G. Haydon, “Physiological astrocytic calcium levels stimulate glutamate release to modulate adjacent

neurons,” Proceedings of the National Academy of Sciences, vol. 97,

no. 15, pp. 8629–8634, 2000. [26] K. Moradi, K. Moradi, M. Ganjkhani, M. Hajihasani, S. Gharibzadeh,

and G. Kaka, “A fast model of voltage-dependent NMDA

receptors,” Journal of computational neuroscience, pp. 1–11, 2013. [27] D. Golomb, C. Yue, and Y. Yaari, “Contribution of persistent Na+

current and M-type K+ current to somatic bursting in CA1 pyramidal

cells: combined experimental and modeling study,” Journal of neurophysiology, vol. 96, no. 4, pp. 1912–1926, 2006.

[28] N. Spruston, P. Jonas, and B. Sakmann, “Dendritic glutamate receptor

channels in rat hippocampal CA3 and CA1 pyramidal neurons.,” The Journal of Physiology, vol. 482, no. Pt 2, pp. 325–352, 1995.

[29] A. E. Steffek, “The Role of Astrocytes in the Pathophysiology of

Schizophrenia,” The University of Michigan, Citeseer, 2007.

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