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bioRxiv preprint doi: https://doi.org/10.1101/2020.04.10.035337; this version posted April 11, 2020. The copyright holder for this preprint (which was not certified by peer review) is the author/funder. All rights reserved. No reuse allowed without permission.

1 Title: Competition for glutamate between NMDA and AMPA receptors prevents 2 runaway synaptic dynamics

3 Abbreviated title: LTP form a negative feedback to itself

4 Qingchen Guoa,b*(郭庆臣)

5 Author affiliation: a Jiangsu Province Key Laboratory of Anesthesiology

6 and Jiangsu Province Key Laboratory of and Analgesia Application 7 Technology, Xuzhou Medical university, Xuzhou 221004, China;

8 Corresponding author: * To whom correspondence should be addressed.

9 E-mail: [email protected] 10

11 Abstract

12 Homeostatic plasticity is an important guarantee for proper neural function. 13 However , long term potentiation (LTP) was thought of as positive feedback in Hebbian 14 plasticity. In this condition, after potentiation is prone to be further potentiated. 15 This can cause runaway dynamics of synapse and affect the stability of neural network. 16 In order to prevent runaway synaptic dynamics, negative feedback is needed. Upon 17 induction of LTP, the α-amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid (AMPA) 18 receptors was increased in the (PSD). Due to the competition for 19 glutamate between AMPA receptors and N-Methyl-D- (NMDA) receptors, 20 the number of opened NMDA channels will reduce. Since the induction of 21 LTP is NMDA receptors dependent, reduction of the number of activated NMDA 22 receptors will increase the threshold of LTP induction. So the LTP of synapse itself can 23 form a negative feedback to LTP induction. To test this hypothesis, a synaptic model 24 with NMDA receptors and AMPA receptors coexisted was developed. When the 25 number of AMPA receptors was increased in the PSD, the number of opened NMDA 26 receptors was reduced though the same number of glutamate was released from 27 presynaptic terminal. This will increase the threshold of further LTP induction and 28 stability of synapse and neural network. 29

30 Keywords: NMDA receptor, AMPA receptor, glutamate, LTP, Homeostatic plasticity

31 32 33 34 35 bioRxiv preprint doi: https://doi.org/10.1101/2020.04.10.035337; this version posted April 11, 2020. The copyright holder for this preprint (which was not certified by peer review) is the author/funder. All rights reserved. No reuse allowed without permission.

1 Introduction

2 Long term change of synaptic transmission has a crucial role in and (1). 3 A widely accepted model of learning and memory is Hebbian plasticity: LTP and LTD (2). LTP 4 and LTD induction are NMDA receptors and activity dependent (3). NMDA receptors are 5 permeable(4). Either LTD or LTP can be induced by the same pattern of stimulation

6 depending on the level of depolarization of the postsynaptic (5). The level of

7 postsynaptic calcium may control the direction of long term plasticity (6, 7). Correlated activity 8 of presynaptic terminal and postsynaptic neuron is needed for induction of long term plasticity 9 (8, 9). A synapse undergo potentiation may have higher probability to to postsynaptic 10 spikes and increase the correlated activity of presynaptic terminal and postsynaptic neuron. 11 This synapse is prone to be further potentiated. This form a kind of positive feedback. The long 12 term plasticity may induce runaway synaptic dynamics (10-12). But in real , 13 the neuron and network activity are kept relatively stable (13, 14). 14 Homeostatic plasticity is mechanisms to keep the synaptic and neuronal network 15 dynamics within a computationally optimal range(13). Both local and overall homeostatic 16 regulation have been observed (15). A lot of mechanisms have been discovered for the 17 homeostatic plasticity(11). But the mechanism of why the won’t get out of 18 control with Hebbian plasticity is still not clearly described. 19 To study the property of synapse after LTP induction, a model of single synapse was 20 developed. The results indicate LTP itself can form a negative feedback to the threshold of LTP 21 induction. This result is conflicted with previous thought that LTP is positive feedback and can 22 cause runaway synaptic dynamics. When LTP was induced in a synapse, the number of AMPA 23 receptors in the PSD was increased. Since AMPA receptors and NMDA receptors can both bind 24 glutamate, they will compete for transmitter. Then the number of opened NMDA receptor 25 channels will decrease. The threshold of LTP induction will be increased. This can prevents 26 runaway synaptic dynamics.

27 Materials and Methods

28 A model of glutamatergic synapse with AMPA receptors and NMDA receptors coexisted 29 in the PSD was developed. The model consist of the glutamate release from presynaptic 30 terminal, the diffusion of glutamate in the synaptic cleft and the interaction of glutamate and 31 postsynaptic receptors. The model was run in the GNU Octave software. The parameters used 32 in the model are list in Table1 (16, 17).

33 Glutamate release and diffusion

34 The release of transmitter from presynaptic terminal is due to the fusion of synaptic vesicle 35 with the presynaptic membrane (18). This fusion can form a fusion pore (19). The transmitter 36 in the synaptic vesicle can diffuse out from this fusion pore. For simplicity, the fusion pore is 37 simulated as a point source and located at the center of the presynaptic membrane. The decay 38 kinetics of glutamate in fused vesicle is taken as an exponential function. The time constant of

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1 glutamate concentration decrease τ in the vesicle is set to 100μs.

d[][] Gluvesicle Glu vesicle 2  (1) dt  3 The synaptic cleft was simulated by a flat cylinder with a height of 20nm and radius of 4 300nm (z, r). The diffusion coefficient of glutamate in the synaptic cleft is 0.25μm2/ms 5 (17).The diffusion function of glutamate is reduced to two dimensional due to the symmetry of 6 cylinder. 22 [][][][]Glucleft1  Glu cleft  Glu cleft  Glu cleft 7 D*()   (2) t r  r  r22  z 8 The synaptic cleft are surrounded by glia cell, so the glutamate cannot diffuse out. The 9 glia cell and the presynaptic terminal can uptake glutamate (20, 21).

10 The kinetics of glutamate and receptor interaction

11 When glutamate diffused to the postsynaptic region, glutamate can bind to postsynaptic 12 receptors. The binding kinetics of glutamate to NMDA receptors and AMPA receptors are 13 adopted from Holmes’s model(17). The kinetics are schemed in Fig. 1. Both the AMPA 14 receptors and NMDA receptors have two binding sites of glutamate. The receptors can be 15 opened or desensitized by the binding of glutamate. The density of AMPA receptors and 16 NMDA receptors are 800/μm2 and 1200/μm2 separately (16). Both AMPA receptors and 17 NMDA receptors are evenly distributed in the PSD. For simplicity, the block of NMDA 18 receptors by is not considered.

19 Results

20 Non-saturation of receptors and competition between NMDA

21 receptors and AMPA receptors for glutamate

22 Both AMPA receptors and NMDA receptors are glutamate receptors (22). The number of 23 transmitter is variable per vesicle and the postsynaptic response of AMPA receptors can range 24 from several picoamps to more than one hundred picoamps (23, 24). So the glutamate receptors 25 can sense variable concentration of glutamate. It is useful to determine whether glutamate can 26 saturate the postsynaptic receptors and the relation between the response of receptors and 27 number of glutamate released from presynaptic terminal. Using the synaptic model, the 28 relationship between the number of glutamate released from presynaptic terminal and synaptic 29 response was tested. The response of AMPA receptors and NMDA receptors increase following 30 the increase of glutamate released from presynaptic terminal. But the increment of the response 31 of receptors get smaller with the same amount of increment of glutamate due to the saturation 32 of receptors (Fig.2A). The estimated number of glutamate per vesicle is about 2000 (25). The 33 postsynaptic receptors are not saturated by this concentration of glutamate. This indicate that 34 single package of glutamate cannot saturate postsynaptic receptors. This result is consist with 3 / 11

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1 previous reports that single package of glutamate cannot saturate postsynaptic receptors (26, 2 27). The glutamate sensitivity and affinity are different between AMPA receptors and NMDA 3 receptors (Fig.2B). 4 In the PSD, AMPA receptors and NMDA receptors coexist and they are both glutamate 5 receptors. Since single package of glutamate cannot saturate postsynaptic receptors, these two 6 types of receptors may compete for glutamate. The response of one type of receptors can be 7 affected by the other. To study how these two types of receptors affect each other, only one 8 type of receptors was placed in the postsynaptic side in the model. The relation between the 9 number of glutamate released from presynaptic terminal and the number of opened receptor 10 channels with only one type of receptors placed in the PSD was obtained. Compared to the 11 condition of two types of receptors coexist, the response of just single type of receptors is 12 bigger (Fig., D). Since the density of AMPA receptors is larger than NMDA receptors, the 13 response of NMDA receptors are more severely affected by AMPA receptors.

14 Negative feedback of Hebbian plasticity

15 LTP and LTD are cellular processes that are involved in learning and memory. AMPA 16 receptors and NMDA receptors coexist in the PSD and both of them can undergo long term 17 plasticity (28, 29). But long term plasticity of AMPA receptors is mostly widely observed. Only 18 the long term plasticity of AMPA receptors was considered in this work. Since AMPA receptors 19 and NMDA receptors are both glutamate receptors. Increasing one type of receptors can reduce 20 the response of the other. How long term plasticity of AMPA receptors will affect the response 21 of NMDA receptors? In the model, the density of AMPA receptors was increased one fold to 22 simulate the effect of LTP. The response of the AMPA receptors was increased almost one fold 23 (Fig.3A). But the response of NMDA receptors was decreased due to the competition for 24 glutamate between AMPA receptors and NMDA receptors (Fig.3B). So LTP can enhance the 25 synaptic weight, but the response of NMDA receptors was reduced. The activation of NMDA 26 receptors is necessary for induction of long term plasticity. This indicate induction of LTP can 27 increase the threshold of further LTP induction. So long term plasticity can form negative 28 feedback to itself. This will prevent runaway synaptic dynamics. This mechanism may play an 29 important role in homeostatic plasticity of synapse. To test how the density of AMPA receptors 30 change affect the response of NMDA receptors, the density of NMDA receptors was kept at 31 800/μm2 and the density of AMPA receptors ranged from 500/μm2 to 5000/μm2. Increasing the 32 density of AMPA receptors, the response of AMPA receptors increased nearly linearly. While 33 the response of NMDA receptors was decreased following the increase of the density of AMPA 34 receptors (Fig.3C). 35 The negative feedback of LTP is due to the competition of AMPA receptors and NMDA 36 receptors for the same transmitter. So glutamate concentration released from presynaptic 37 terminal will affect the weight of this negative feedback. Physiologically, the number of single 38 package of transmitter are variable and can be regulated. How the quantal size will affect the 39 negative feedback effect of long term plasticity? To test this effect, the glutamate number per 40 vesicle ranged from 500 to 5000 per vesicle in the model. Increasing the number of glutamate 41 reduced the difference of the response of NMDA receptors between the control one and the 42 LTP of AMPA receptors (Fig.4B). When the glutamate can totally saturate postsynaptic

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1 receptors, the competition between AMPA receptors and NMDA receptors for glutamate get 2 negligible. 3 There are evidences that the NMDA receptors and AMPA receptors are non- 4 homogeneously distributed in the PSD (30-32). AMPA receptors are denser at the periphery of 5 the PSD and the density of NMDA receptors is highest at the center of the PSD. To test how 6 the different distributions of AMPA receptors and NMDA receptors affect the competition for 7 glutamate. The distribution of NMDA receptors are set as a gaussian distribution with the 8 highest density at the center of PSD and the standard deviation is 0.1μm. The distribution of 9 AMPA receptors is also gaussian distribution with the highest density located at 0.15μm to the 10 center of PSD and the standard deviation is half of the distribution of NMDA receptors (Fig.5A). 11 The results show even the distribution of AMPA receptors and NMDA receptors are different, 12 the competition for glutamate are still exist. After the LTP of AMPA receptors, the response of 13 NMDA receptors was reduced (Fig.5C).

14 Synaptic enlargement enhance negative feedback of LTP

15 Following synaptic strength enhancement after LTP induction, the structure of synapse 16 will also change (33, 34). To simulate this effect, the area of the PSD was increased one fold 17 in the model. The density of AMPA receptors and the total number of NMDA receptors 18 remained unchanged. Since the area of the PSD was increased, the density of NMDA receptors 19 was decreased as well. The result show the decrement of the response of NMDA receptors after 20 LTP of AMPA receptors was larger compared to the density change of AMPA receptors 21 (Fig.6A). But the increment of the response of AMPA receptors after LTP of AMPA receptors 22 is smaller than in the condition of increasing the density of AMPA receptors in the PSD (Fig.6B). 23 One reason is synaptic cleft was also enlarged, so the concentration of glutamate was reduced 24 in the synaptic cleft. Another is the density of NMDA receptors was reduced due to the 25 enlargement of PSD. So the enlargement of synapse will enhance the negative feedback of long 26 term plasticity of AMPA receptors. The decrement of the response of NMDA receptors is also 27 glutamate concentration dependent in this condition (Fig.6C). Increasing the number of 28 glutamate released from presynaptic terminal decreased the difference of the response of 29 NMDA receptors between the control one and LTP of AMPA receptors. When glutamate can 30 totally saturate postsynaptic receptors, the competition between AMPA receptors and NMDA 31 receptors get negligible.

32 Discussion

33 A great diversity of plasticity has been discovered in nervous system and they are likely 34 governed by independent mechanisms (35). Homeostatic plasticity is an important mechanism 35 to preserve stable electrophysiological properties of neuron. In recent years, important progress 36 has been made toward identifying molecules and signaling processes required for homeostatic 37 forms of . A new mechanism of homeostatic plasticity was provided in this work. 38 In glutamatergic synapse, the AMPA receptors and NMDA receptors can affect each other due 39 to the competition for the same transmitter. It is usually thought that Hebbian plasticity is 40 positive feedback and can cause runaway synaptic dynamics. This work indicate that LTP is a

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1 negative feedback to the threshold of LTP induction. Induction of LTP can increase the 2 threshold of further LTP induction. This negative feedback is due to the competition for 3 glutamate between AMPA receptors and NMDA receptors. This may be a new mechanism of 4 homeostatic plasticity and can prevents runaway synaptic dynamics. 5 The competition of AMPA receptors and NMDA receptors for glutamate is based on the 6 result that the postsynaptic receptors are not saturated by glutamate released from presynaptic 7 terminal. If the glutamate can saturate postsynaptic receptors, the competition effect of NMDA 8 receptors and AMPA receptors will be eliminated. By now there are a lot of experimental results 9 show the postsynaptic receptors are not saturated by transmitter (27, 36, 37). Functionally, no 10 saturation of receptors can provide more dynamic space for the regulation of synaptic function. 11 So it is reasonable to think that the postsynaptic receptors are not saturated by moderate activity 12 of synapse. 13 An important factor that affect the negative feedback of LTP is the number of glutamate 14 released from presynaptic terminal. In the model, the number of glutamate per vesicle is 15 adopted from Rusakov’s estimate (25). The real number of glutamate per vesicle is still not 16 determined. But it is confirmed that the number of glutamate are variable and can be regulated 17 by the activity of synapse (38, 39). If the number of glutamate released from presynaptic 18 terminal is smaller, the negative feedback of LTP will get larger. 19 The negative feedback of LTP to the threshold of LTP induction is based on that only the 20 number of AMPA receptors in the PSD was increased after induction of LTP. There is report 21 that the induction of long term potentiation will increase NMDA receptors and AMPA receptors 22 proportionally. But the increase of NMDA receptors is slower than AMPA receptors (40). The 23 proportional change of AMPA receptors and NMDA receptors can eliminate the effect of 24 negative feedback of LTP. But there are also evidences conflicted with the proportional increase 25 of AMPA receptors and NMDA receptors in the LTP induction of AMPA receptors. In nucleus 26 accumbens, induction of calcium dependent LTP of non-NMDA receptors will produce a 27 simultaneous LTD of NMDA receptors (41). This will enhance the negative feedback of LTP. 28 In the dentate gyrus, the NMDA receptors increase during development, but the ratio of NMDA 29 receptors to AMPA receptors decrease (42). In during development, the silent 30 synapse acquired AMPA receptors with little change of NMDA receptors (43). There is also 31 evidence that the NMDA receptors mediated current decrease while the response of AMPA 32 receptors increase at an auditory synapse during development (44). So it is reasonable to think 33 that NMDA receptors receptor will not increase after LTP induction of AMPA receptors. LTP 34 of AMPA receptors can reduce the response of NMDA receptors, also LTD of AMPA receptors 35 can increase the response of NMDA receptors. So the overall ratio of the response of AMPA 36 receptors and NMDA receptors may still keep constant.

37 Acknowledgements

38 References

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16 Figure Legends

17 Fig.1 The kinetics of glutamate and NMDA receptors and AMPA receptors interaction. (A) The 18 kinetics of glutamate binding to NMDA receptors. NMDAR represents NMDA receptor, Glu 19 represents glutamate. NMDAR * indicate the opened state of NMDA receptor channel and 20 NMDAR_D is desensitized state of NMDA receptor. The block of NMDA receptors by 21 magnesium is not considered. (B) Kinetics of glutamate binding to AMPA receptors. AMPAR 22 represents AMPA receptors, AMPAR* is the opened state of AMPA receptor channel and 23 AMPAR_D is the desensitized state of AMPA receptor. 24 25 Fig.2 Non-saturation of receptors and competition between NMDA receptors and AMPA 26 receptors for glutamate. (A) The relation of the number of opened AMPA receptors and NMDA 27 receptors and the number of glutamate released from presynaptic terminal with these two types 28 of receptors coexist. The red line is the peak number of opened AMPA receptor channels, the 29 blue line is the peak number of opened NMDA receptor channels. (B) Normalized relation of 30 opened AMPA receptors and NMDA receptors and the number of glutamate released from 31 presynaptic terminal with these two types of receptors coexist. (C) Glutamate sensitivity of 32 AMPA receptors without the affection of NMDA receptors. The solid line is the peak number 33 of opened AMPA receptor channels with AMPA receptors and NMDA receptors coexist. The 34 dotted line is the peak number of opened AMPA receptor channels with only AMPA receptors 35 in the PSD. (D) Glutamate sensitivity of NMDA receptors without the affection of AMPA 36 receptors. The solid line is the peak number of opened NMDA receptor channels with AMPA 37 receptors and NMDA receptors coexist. The dotted line is the peak number of opened NMDA 38 receptor channels with only NMDA receptors in the PSD. 39 40 Fig.3 Negative feedback of LTP induction. (A) The response of AMPA receptors before and 41 after LTP of AMPA receptors. The solid line is the response of AMPA receptors before LTP and 42 the dotted line is the response of AMPA receptors after LTP (increase the density of AMPA

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1 receptors one fold). (B) The response of NMDA receptors before and after LTP of AMPA 2 receptors. The solid line is the response of NMDA receptors before LTP of AMPA receptors, 3 the dotted line is the response of NMDA receptors after LTP of AMPA receptors. (C) Relation 4 between peak number of activated AMPA receptors and NMDA receptors and the density of 5 AMPA receptors when the density of NMDA receptors was kept unchanged. The red line is the 6 peak number of opened AMPA receptors, the blue line is the peak number of opened NMDA 7 receptors. 8 9 Fig.4 The weight of negative feedback of LTP is affected by glutamate concentration. (A) 10 Sample traces of the response of NMDA receptors before and after LTP of AMPA receptors 11 with different numbers of glutamate released from presynaptic terminal. (A1) 1000 glutamate 12 per vesicle, (A2) 2000 glutamate per vesicle, (A3) 3000 glutamate per vesicle. (B) Dependence 13 of the reduction of the response of NMDA receptors on the number of glutamate released from 14 presynaptic terminal. 15 16 Fig.5 Non-homogenous distribution of AMPA receptors and NMDA receptors does not 17 eliminate the competition for glutamate. (A) The distribution of AMPA receptors and NMDA 18 receptors in the PSD. (B) The response of AMPA receptors before and after LTP induction 19 (increase the density of AMPA receptors one fold). (C) The response of NMDA receptors 20 before and after the LTP of AMPA receptors. 21 22 Fig.6 The effect of synaptic structure change after LTP induction. (A) The response of AMPA 23 receptors before and after LTP of AMPA receptors. The solid line is the response of AMPA 24 receptors before LTP and the dotted line is the response of AMPA receptors after LTP (the area 25 of PSD was increased one fold, the density of AMPA receptors and the total number of NMDA 26 receptors was not changed). (B) The response of NMDA receptors before and after LTP of 27 AMPA receptors. The solid line is the response of NMDA receptors before LTP of AMPA 28 receptors, the dotted line is the response of NMDA receptors after LTP of AMPA receptors. (C) 29 The dependence of the reduction of the response of NMDA receptors on the number of 30 glutamate released from presynaptic terminal.

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1 Table 1 Parameters used in the model

2

Parameter Symbol Value Glutamate diffusion coeff. D 0.25μm2/ms Uptake affinity(terminal) 2μM Uptake capacity(terminal) Vmax 160μM /ms Uptake rate(glia) 60/ms AMPA receptors density 800/μm2 NMDA receptors density 1200/μm2 AMPA receptors binding Kon1 0.00918/μM/ms Koff1 8.52/ms Kon2 0.0568/μM/ms Koff2 6.52/ms Kon3 0.00254/μM/ms Koff3 0.0914/ms α 1.8/ms β 8.5/ms α1 0.0784/ms β1 5.78/ms α2 0.01454/ms β2 0.344/ms α3 0.008/ms β3 0.0354.ms α4 0.3808/ms β4 0.0336/ms NMDA receptors binding kon 0.00918/μM/ms koff 0.0067/ms α 0.20/ms β 0.06/ms kd1 0.01/ms kd2 0.01/ms kr1 0.002/ms kr2 0.002/ms

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