The Influence of Synaptic Size on AMPA Receptor Activation: A Monte Carlo Model

Physiological and electron microscope studies have shown that synapses are functionally and morphologically heterogeneous and that variations in size of synaptic junctions are related to characteristics such as release probability and density of postsynaptic AMPA receptors. The present article focuses on how these morphological variations impact synaptic transmission. We based our study on Monte Carlo computational simulations of simplified model synapses whose morphological features have been extracted from hundreds of actual synaptic junctions reconstructed by three-dimensional electron microscopy. We have examined the effects that parameters such as synaptic size or density of AMPA receptors have on the number of receptors that open after release of a single synaptic vesicle. Our results indicate that the maximum number of receptors that will open after the release of a single synaptic vesicle may show a ten-fold variation in the whole population of synapses. When individual synapses are considered, there is also a stochastical variability that is maximal in small synapses with low numbers of receptors. The number of postsynaptic receptors and the size of the synaptic junction are the most influential parameters, while the packing density of receptors or the concentration of extrasynaptic transporters have little or no influence on the opening of AMPA receptors.     

Stochastic model of central synapses: slow diffusion of transmitter interacting with spatially distributed receptors and transporters.

A detailed mathematical analysis of the diffusion process of neurotransmitter inside the synaptic cleft is presented and the spatio-temporal concentration profile is calculated. Using information about the experimentally observed time course of glutamate in the cleft the effective diffusion coefficient Dnet is estimated as Dnet approximately 20-50 nm(2) microseconds(-1), implying a strong reduction compared with free diffusion in aqueous solution. The tortuosity of the cleft and interactions with transporter molecules are assumed to affect the transmitter motion. We estimate the transporter density to be 5170 to 8900 micrometer(-2) in the synaptic cleft and its vicinity, using the experimentally observed time constant of glutamate. Furthermore a theoretical model of synaptic transmission is presented, taking the spatial distribution of post-synaptic (AMPA-) receptors into account. The transmitter diffusion and receptor dynamics are modeled by Monte Carlo simulations preserving the typically observed noisy character of post-synaptic responses. Distributions of amplitudes, rise and decay times are calculated and shown to agree well with experiments. Average open probabilities are computed from a novel kinetic model and are shown to agree with averages over many Monte Carlo runs. Our results suggest that post-synaptic currents are only weakly potentiated by clustering of post-synaptic receptors, but increase linearly with the total number of receptors. Distributions of amplitudes and rise times are used to discriminate between different morphologies, e.g. simple and perforated synapses. A skew in the miniature amplitude distribution can be caused by multiple release of pre-synaptic vesicles at perforated synapses.     

Glutamate escape from a tortuous synaptic cleft of the hippocampal mossy fibre synapse

The time course of neurotransmitter in the synaptic cleft contributes substantially to the fast kinetics of synaptic signalling. Hippocampal mossy fibres (MFs), a well-characterised excitatory pathway from dentate granule cells to the hippocampus proper, form large glutamatergic synapses at branched spiny structures in CA3 pyramidal cell dendrites. To what extent transmission at these synapses is affected by retarded glutamate clearance from the large tortuous synaptic cleft is not known. Here, we propose a simple geometrical approximation representing the 'typical' geometry of thorny excrescences that form the tortuous cleft interface at a MF synapse. We then employ Monte Carlo simulations to monitor movements of 3000 individual glutamate molecules released within the cleft. The results predict that, in the absence of neuronal glutamate transporters, it should take approximately 10 ms for 50% and 60-70 ms for 90% of glutamate molecules to escape the MF synapse.     

Neurobeachin regulates neurotransmitter receptor trafficking to synapses

The surface density of neurotransmitter receptors at synapses is a key determinant of synaptic efficacy. Synaptic receptor accumulation is regulated by the transport, postsynaptic anchoring, and turnover of receptors, involving multiple trafficking, sorting, motor, and scaffold proteins. We found that neurons lacking the BEACH (beige-Chediak/Higashi) domain protein Neurobeachin (Nbea) had strongly reduced synaptic responses caused by a reduction in surface levels of glutamate and GABA_A receptors. In the absence of Nbea, immature AMPA receptors accumulated early in the biosynthetic pathway, and mature N-methyl-d-aspartate, kainate, and GABA_A receptors did not reach the synapse, whereas maturation and surface expression of other membrane proteins, synapse formation, and presynaptic function were unaffected. These data show that Nbea regulates synaptic transmission under basal conditions by targeting neurotransmitter receptors to synapses.     

A Dynamic Corral Model of Receptor Trafficking at a Synapse

The postsynaptic density (PSD) is a cytoskeletal specialization within the postsynaptic membrane of a neuron that helps to concentrate and organize neurotransmitter receptors at a chemical synapse. The total number of receptors within the PSD, which is a major factor in determining the physiological strength or weight of a synapse, fluctuates due to the surface diffusion of receptors into and out of the PSD, and the interactions of receptors with scaffolding proteins and cytoskeletal elements within the PSD. In this article, we present a stochastic model of protein receptor trafficking at the PSD that takes into account these various processes. The PSD is treated as a stochastically gated corral, which contributes a source of extrinsic or environmental noise that supplements the intrinsic noise arising from small receptor numbers. Using a combination of stochastic analysis and Monte Carlo simulations, we determine the time-dependent variation in the mean and variance of synaptic receptor numbers for a variety of initial conditions that simulate fluorescence recovery after photobleaching experiments, and indicate how such data might be used to infer certain properties of the PSD.     

Metadynamic sampling of the free-energy landscapes of proteins coupled with a Monte Carlo algorithm

Metadynamics is a powerful computational tool to obtain the free-energy landscape of complex systems. The Monte Carlo algorithm has proven useful to calculate thermodynamic quantities associated with simplified models of proteins, and thus to gain an ever-increasing understanding on the general principles underlying the mechanism of protein folding. We show that it is possible to couple metadynamics and Monte Carlo algorithms to obtain the free energy of model proteins in a way which is computationally very economical.     

Molecular dynamics of postsynaptic receptors and scaffold proteins

The activity of neurotransmitter receptors determines the strength of synaptic transmission. Therefore, the clustering of receptors at synapses is an important mechanism underlying synaptic plasticity. The dynamic exchange of receptors between synaptic and extrasynaptic membranes is dependent on their interaction with synaptic scaffold proteins. Here, we review the recent advances and emerging concepts related to the dynamics of synaptic proteins at inhibitory and excitatory synapses. These include the imaging techniques that enable the study of protein dynamics in cells, the differences and similarities of receptor dynamics at excitatory and inhibitory synapses, the relationship between the exchange of receptor and scaffold proteins, as well as the role of receptor fluxes in the modulation of synaptic strength.     

Automating human intuition for protein design

In the design of new enzymes and binding proteins, human intuition is often used to modify computationally designed amino acid sequences prior to experimental characterization. The manual sequence changes involve both reversions of amino acid mutations back to the identity present in the parent scaffold and the introduction of residues making additional interactions with the binding partner or backing up first shell interactions. Automation of this manual sequence refinement process would allow more systematic evaluation and considerably reduce the amount of human designer effort involved. Here we introduce a benchmark for evaluating the ability of automated methods to recapitulate the sequence changes made to computer‐generated models by human designers, and use it to assess alternative computational methods. We find the best performance for a greedy one‐position‐at‐a‐time optimization protocol that utilizes metrics (such as shape complementarity) and local refinement methods too computationally expensive for global Monte Carlo (MC) sequence optimization. This protocol should be broadly useful for improving the stability and function of designed binding proteins. Proteins 2014; 82:858–866. © 2013 Wiley Periodicals, Inc.     

Population rate coding in recurrent neuronal networks with unreliable synapses

Neuron transmits spikes to postsynaptic neurons through synapses. Experimental observations indicated that the communication between neurons is unreliable. However most modelling and computational studies considered deterministic synaptic interaction model. In this paper, we investigate the population rate coding in an all-to-all coupled recurrent neuronal network consisting of both excitatory and inhibitory neurons connected with unreliable synapses. We use a stochastic on-off process to model the unreliable synaptic transmission. We find that synapses with suitable successful transmission probability can enhance the encoding performance in the case of weak noise; while in the case of strong noise, the synaptic interactions reduce the encoding performance. We also show that several important synaptic parameters, such as the excitatory synaptic strength, the relative strength of inhibitory and excitatory synapses, as well as the synaptic time constant, have significant effects on the performance of the population rate coding. Further simulations indicate that the encoding dynamics of our considered network cannot be simply determined by the average amount of received neurotransmitter for each neuron in a time instant. Moreover, we compare our results with those obtained in the corresponding random neuronal networks. Our numerical results demonstrate that the network randomness has the similar qualitative effect as the synaptic unreliability but not completely equivalent in quantity.     

CPG2: a brain- and synapse-specific protein that regulates the endocytosis of glutamate receptors

Long-term maintenance and modification of synaptic strength involve the turnover of neurotransmitter receptors. Glutamate receptors are constitutively and acutely internalized, presumptively through clathrin-mediated receptor endocytosis. Here, we show that cpg2 is a brain-specific splice variant of the syne-1 gene that encodes a protein specifically localized to a postsynaptic endocytotic zone of excitatory synapses. RNAi-mediated CPG2 knockdown increases the number of postsynaptic clathrin-coated vesicles, some of which traffic NMDA receptors, disrupts the constitutive internalization of glutamate receptors, and inhibits the activity-induced internalization of synaptic AMPA receptors. Manipulating CPG2 levels also affects dendritic spine size, further supporting a function in regulating membrane transport. Our results suggest that CPG2 is a key component of a specialized postsynaptic endocytic mechanism devoted to the internalization of synaptic proteins, including glutamate receptors. The activity dependence and distribution of cpg2 expression further suggest that it contributes to the capacity for postsynaptic plasticity inherent to excitatory synapses.     

Visualization of synaptic vesicle movement in intact synaptic boutons using fluorescence fluctuation spectroscopy

Not much is known about the mobility of synaptic vesicles inside small synapses of the central nervous system, reflecting a lack of methods for visualizing these dynamics. We adapted confocal spot detection with fluctuation analysis to monitor the mobility of fluorescently labeled synaptic vesicles inside individual boutons of cultured hippocampal neurons. Using Monte Carlo simulations we were able to propose a simple quantitative model that can describe vesicle mobility in small hippocampal boutons under resting conditions and different pharmacological treatments. We find that vesicle mobility in a time window of 20 s can be well described by caged diffusion (D approximately 5 x 10(-5) microm(2)/s, cage sizes of approximately 50 nm). Mobility can be upregulated by phosphatase blockage and increased further by actin disruption in a dose-dependent manner. Inhibition of the myosin light chain kinase slows down vesicle mobility 10-fold, whereas other kinases like protein kinase C (PKC), A (PKA), and calmodulin kinase II (caMKII) do not affect mobility in unstimulated boutons.     

Astrocytes optimize the synaptic transmission of information

Chemical synapses transmit information via the release of neurotransmitter-filled vesicles from the presynaptic terminal. Using computational modeling, we predict that the limited availability of neurotransmitter resources in combination with the spontaneous release of vesicles limits the maximum degree of enhancement of synaptic transmission. This gives rise to an optimal tuning that depends on the number of active zones. There is strong experimental evidence that astrocytes that enwrap synapses can modulate the probabilities of vesicle release through bidirectional signaling and hence regulate synaptic transmission. For low-fidelity hippocampal synapses, which typically have only one or two active zones, the predicted optimal values lie close to those determined by experimentally measured astrocytic feedback, suggesting that astrocytes optimize synaptic transmission of information.     

Clustering of AMPA receptors by the synaptic PDZ domain-containing protein PICK1

Synaptic clustering of neurotransmitter receptors is crucial for efficient signal transduction and integration in neurons. PDZ domain-containing proteins such as PSD-95/SAP90 interact with the intracellular C termini of a variety of receptors and are thought to be important in the targeting and anchoring of receptors to specific synapses. Here, we show that PICK1 (protein interacting with C kinase), a PDZ domain-containing protein, interacts with the C termini of alpha-amino-3-hydroxy-5-methyl-isoxazole-4-propionic acid (AMPA) receptors in vitro and in vivo. In neurons, PICK1 specifically colocalizes with AMPA receptors at excitatory synapses. Furthermore, PICK1 induces clustering of AMPA receptors in heterologous expression systems. These results suggest that PICK1 may play an important role in the modulation of synaptic transmission by regulating the synaptic targeting of AMPA receptors.     

Molecules involved in the formation of synaptic connections in muscle and brain.

Synapses are highly specialized structures designed to guarantee precise and efficient communication between neurons and their target cells. Molecules of the extracellular matrix have an instructive role in the formation of the neuromuscular junction, the best-characterized synapse. In this review, the molecular mechanisms underlying these instructive signals will be discussed with particular emphasis on the receptors involved. Additionally, recent evidence for the involvement of specific adhesion complexes in the formation and modulation of synapses in the central nervous system will be reviewed. Synapses are specialized junctions between neurons and their target cells where information is transferred from the pre- to the postsynaptic cell. At most vertebrate synapses, this transfer is accomplished by the release of a specific neurotransmitter from the presynaptic nerve terminal. The release of neurotransmitter is initiated by the action potential and the subsequent influx of Ca(2+) into the presynaptic nerve terminal. This results in the rapid fusion of vesicles with the nerve membrane and the release of the neurotransmitter into the synaptic cleft. The neurotransmitter then diffuses across the cleft and binds to specific postsynaptic receptors, resulting in a change in the membrane potential of the postsynaptic cell. This can result in the generation of an action potential. The high precision of synaptic transmission requires that pre- and postsynaptic structures are both highly organized and in juxtaposition to each other. In addition, alterations in synaptic transmission are the basis of learning and memory and are likely to be accompanied by the remodeling of synaptic structures (Toni et al., 1999). Thus, the study of how synapses are formed during development is also of relevance for the understanding of the cellular and molecular processes involved in learning and memory. This review focuses on the molecular mechanisms involved in the formation and the function of synapses.     

Organization and regulation of proteins at synapses

The organization and regulation of synaptic connections in the mammalian nervous system entail complicated and co-ordinated molecular and cellular processes. The unveiling of various protein-protein interactions and their functional consequences at synapses have led to a greater understanding of the process of synapse formation and the modulation of synaptic transmission. Recent studies indicate that the major excitatory neurotransmitter receptors in the brain, the glutamate receptors, are associated with many different molecules that are involved in the formation of elaborate synaptic cytoskeletal networks and signal transduction cascades. These complex protein networks may play critical roles in the regulation of neurotransmitter receptor function and the efficacy of synaptic transmission.     

Neuregulin: An activity-dependent synaptic modulator at the neuromuscular junction

Synaptic activity in the form of neurotransmitter release and postsynaptic depolarization is a prime motive force that guides synaptic development throughout the nervous system. The molecular basis of how synaptic activity is converted into structural changes that build and maintain synapses is a key question that has recently become focused on regulatory factors that act on tyrosine kinase receptors on both sides of the synaptic interface. The neuregulins are such a family of growth and differentiation factors that exist as both membrane-bound and soluble forms through alternatively splicing. Neuregulin functions to promote the local expression of acetylcholine receptors at neuromuscular synapses and therefore has the potential to strengthen specific synaptic connections. Recent evidence suggests that synaptic activity at the neuromuscular junction is coupled to presynaptic neuregulin release through an indirect mechanism acting through the postsynaptic expression of neurotrophic factors. At early stages of development, this could potentiate the stability of more active synapses. Later in development, heparin-binding forms of neuregulin accumulate to high levels in the synaptic basal lamina through the developmentally programmed expression of heparan sulfate proteoglycans, thus providing a sustained source of neuregulin to the most active synapses.     

The actions of synaptically released zinc at hippocampal mossy fiber synapses

Zn2+ is present at high concentrations in the synaptic vesicles of hippocampal mossy fibers. We have used Zn2+ chelators and the mocha mutant mouse to address the physiological role of Zn2+ in this pathway. Zn2+ is not involved in the unique presynaptic plasticities observed at mossy fiber synapses but is coreleased with glutamate from these synapses, both spontaneously and with electrical stimulation, where it exerts a strong modulatory effect on the NMDA receptors. Zn2+ tonically occupies the high-affinity binding site of NMDA receptors at mossy fiber synapses, whereas the lower affinity voltage-dependent Zn2+ binding site is occupied during action potential driven-release. We conclude that Zn2+ is a modulatory neurotransmitter released from mossy fiber synapses and plays an important role in shaping the NMDA receptor response at these synapses.     

Analytical description of the activation of multi-state receptors by continuous neurotransmitter signals at brain synapses.

Chemical synaptic transmission is a fundamental component of interneuronal communications in the central nervous system (CNS). Discharge of a presynaptic vesicle containing a few thousand molecules (a quantum) of neurotransmitter into the synaptic cleft generates a transmitter concentration signal that drives postsynaptic ion-channel receptors. These receptors exhibit multiple states, with state transition kinetics dependent on neurotransmitter concentration. Here, a novel and simple analytical approach for describing gating of multi-state receptors by signals with complex continuous time courses is used to describe the generation of glutamate-mediated quantal postsynaptic responses at brain synapses. The neurotransmitter signal, experienced by multi-state N-methyl-D-aspartate (NMDA)- and L-alpha-amino-3-hydroxy-5-methyl-4-isoxazolepropionate (AMPA)-type glutamate receptors at specific points in a synaptic cleft, is approximated by a series of step functions of different intensity and duration and used to drive a Markovian, multi-state kinetic scheme that describes receptor gating. Occupancy vectors at any point in time can be computed interatively from the occupancy vectors at the times of steps in transmitter concentration. Multi-state kinetic schemes for both the low-affinity AMPA subtype of glutamate receptor and for the high-affinity NMDA subtype are considered, and expected NMDA and AMPA components of synaptic currents are calculated. The amplitude of quantal responses mediated by postsynaptic receptor clusters having specific spatial distributions relative to foci of quantal neurotransmitter release is then calculated and related to the displacement between the center of the postsynaptic receptor cluster and the focus of synaptic vesicle discharge. Using this approach we show that the spatial relation between the focus of release and the center of the postsynaptic receptor cluster affects synaptic efficacy. We also show how variation in this relation contributes to variation in synaptic current amplitudes.