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 The copyright holder for this preprint (which was not certified by peer review) is the author/funder.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 Anesthesia 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, synapse 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 postsynaptic density (PSD). Due to the competition for 19 glutamate between AMPA receptors and N-Methyl-D-aspartic acid (NMDA) receptors, 20 the number of opened NMDA receptor 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 The copyright holder for this preprint (which was not certified by peer review) is the author/funder.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 learning and memory (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 calcium 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 neuron (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 lead 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 nervous system, 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 synaptic weight 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 2 / 11 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 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 magnesium 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 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 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.