A Computational Model for the AMPA Receptor Phosphorylation Master Switch Regulating Cerebellar Long-Term Depression

Biophysical Modeling of Synaptic Plasticity

Dendritic spines are small, bulbous compartments that function as postsynaptic sites and undergo intense biochemical and biophysical activity. The role of the myriad signaling pathways that are implicated in synaptic plasticity is well studied. A recent abundance of quantitative experimental data has made the events associated with synaptic plasticity amenable to quantitative biophysical modeling. Spines are also fascinating biophysical computational units because spine geometry, signal transduction, and mechanics work in a complex feedback loop to tune synaptic plasticity. In this sense, ideas from modeling cell motility can inspire us to develop multiscale approaches for predictive modeling of synaptic plasticity. In this article, we review the key steps in postsynaptic plasticity with a specific focus on the impact of spine geometry on signaling, cytoskeleton rearrangement, and membrane mechanics. We summarize the main experimental observations and highlight how theory and computation can aid our understanding of these complex processes.

Spatiotemporal modelling reveals geometric dependence of AMPAR dynamics on dendritic spine morphology

The modification of neural circuits depends on the strengthening and weakening of synaptic connections. Synaptic strength is often correlated to the density of the ionotropic, glutamatergic receptors, AMPARs, (α-amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid receptors) at the postsynaptic density (PSD). While AMPAR density is known to change based on complex biological signalling cascades, the effect of geometric factors such as dendritic spine shape, size and curvature remain poorly understood. In this work, we developed a deterministic, spatiotemporal model to study the dynamics of AMPARs during long-term potentiation (LTP). This model includes a minimal set of biochemical events that represent the upstream signalling events, trafficking of AMPARs to and from the PSD, lateral diffusion in the plane of the spine membrane, and the presence of an extrasynaptic AMPAR pool. Using idealized and realistic spine geometries, we show that the dynamics and increase of bound AMPARs at the PSD depends on a combination of endo- and exocytosis, membrane diffusion, the availability of free AMPARs and intracellular signalling interactions. We also found non-monotonic relationships between spine volume and the change in AMPARs at the PSD, suggesting that spines restrict changes in AMPARs to optimize resources and prevent runaway potentiation. KEY POINTS: Synaptic plasticity involves dynamic biochemical and physical remodelling of small protrusions called dendritic spines along the dendrites of neurons. Proper synaptic functionality within these spines requires changes in receptor number at the synapse, which has implications for downstream neural functions, such as learning and memory formation. In addition to being signalling subcompartments, spines also have unique morphological features that can play a role in regulating receptor dynamics on the synaptic surface. We have developed a spatiotemporal model that couples biochemical signalling and receptor trafficking modalities in idealized and realistic spine geometries to investigate the role of biochemical and biophysical factors in synaptic plasticity. Using this model, we highlight the importance of spine size and shape in regulating bound AMPA receptor dynamics that govern synaptic plasticity, and predict how spine shape might act to reset synaptic plasticity as a built-in resource optimization and regulation tool.

Technical approaches and challenges to study AMPA receptors in oligodendrocyte lineage cells: Past, present, and future

Receptors for α-amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid (AMPARs) are ligand-gated ionotropic receptors for glutamate that is a major excitatory neurotransmitter in the central nervous system. AMPARs are located at postsynaptic sites of neuronal synapses where they mediate fast synaptic signaling and synaptic plasticity. Remarkably, AMPARs are also expressed by glial cells. Their expression by the oligodendrocyte (OL) lineage cells is of special interest because AMPARs mediate fast synaptic communication between neurons and oligodendrocyte progenitor cells (OPCs), modulate proliferation and differentiation of OPCs, and may also be involved in regulation of myelination. On the other hand, during pathological conditions, AMPARs may mediate damage of the OL lineage cells. In the present review, we focus on the technical approaches that have been used to study AMPARs in the OL lineage cells, and discuss future perspectives of AMPAR research in these glial cells.

Crosstalk between biochemical signalling network architecture and trafficking governs AMPAR dynamics in synaptic plasticity

Synaptic plasticity involves modification of both biochemical and structural components of neurons. Many studies have revealed that the change in the number density of the glutamatergic receptor AMPAR at the synapse is proportional to synaptic weight update; an increase in AMPAR corresponds to strengthening of synapses while a decrease in AMPAR density weakens synaptic connections. The dynamics of AMPAR are thought to be regulated by upstream signalling, primarily the calcium-CaMKII pathway, trafficking to and from the synapse, and influx from extrasynaptic sources. Previous work in the field of deterministic modelling of CaMKII dynamics has assumed bistable kinetics, while experiments and rule-based modelling have revealed that CaMKII dynamics can be either monostable or ultrasensitive. This raises the following question: how does the choice of model assumptions involving CaMKII dynamics influence AMPAR dynamics at the synapse? To answer this question, we have developed a set of models using compartmental ordinary differential equations to systematically investigate contributions of different signalling and trafficking variations, along with their coupled effects, on AMPAR dynamics at the synaptic site. We find that the properties of the model including network architecture describing different stability features of CaMKII and parameters that capture the endocytosis and exocytosis of AMPAR significantly affect the integration of fast upstream species by slower downstream species. Furthermore, we predict that the model outcome, as determined by bound AMPAR at the synaptic site, depends on (1) the choice of signalling model (bistable CaMKII or monostable CaMKII dynamics), (2) trafficking versus influx contributions and (3) frequency of stimulus. KEY POINTS: The density of AMPA receptors (AMPARs) at the postsynaptic density of the synapse provides a readout of synaptic plasticity, which involves crosstalk between complex biochemical signalling networks including CaMKII dynamics and trafficking pathways including exocytosis and endocytosis. Here we build a model that integrates CaMKII dynamics and AMPAR trafficking to explore this crosstalk. We compare different models of CaMKII that result in monostable or bistable kinetics and their impact on AMPAR dynamics. Our results show that AMPAR density depends on the coupling between aspects of biochemical signalling and trafficking. Specifically, assumptions regarding CaMKII dynamics and its stability features can alter AMPAR density at the synapse. Our model also predicts that the kinetics of trafficking versus influx of AMPAR from the extrasynaptic space can further impact AMPAR density. Thus, the contributions of both signalling and trafficking should be considered in computational models.

Mechanisms Underlying Mu Opioid Receptor Effects on Parallel Fiber-Purkinje Cell Synaptic Transmission in Mouse Cerebellar Cortex

μ-opioid receptors (MOR) are widely expressed in the brain, varying in density in different areas. Activation of MORs underlies analgesia, euphoria, but may lead to tolerance, dependence, and ultimately opioid addiction. The Purkinje cell (PC) is the only efferent neuron in the cerebellar cortex and receives glutamatergic synaptic inputs from the parallel fibers formed by the axons of granule cells. Studies have shown that MORs are expressed during the development of cerebellar cells. However, the distribution of MOR and their effects on PF-PC synaptic transmission remain unclear. To examine these questions, we used whole-cell patch clamp recordings and pharmacological methods to determine the effects and mechanisms of MOR activation on synaptic transmission at PF-PC synapses. The MOR-selective agonist DAMGO significantly reduced the amplitude and area under the curve (AUC) of PF-PC evoked (e) EPSCs, and increased the paired-pulse ratio (PPR).DAMGO-induced inhibitory effects on PF-PC eEPSCs and PPR were abolished by MOR specific blocker CTOP. Further, DAMGO significantly reduced the frequency of PF-PC mEPSCs, but had no obvious effect on their amplitude, suggesting a presynaptic site of action. The DAMGO-induced reduction in the frequency of PF-PC mEPSCs also was blocked by CTOP. A protein kinase A (PKA) inhibitor PKI added in the pipette solution did not affect the inhibitory effects on PF-PC mEPSCs induced by DAMGO. Both the PKA inhibitor K5720 and MEK inhibitor U0126 in artificial cerebrospinal fluid (ACSF) prevented the inhibitory effects of DAMGO on PF-PC mEPSCs. These findings reveal that MORs are expressed in presynaptic PF axon terminals, where DAMGO can activate presynaptic MORs to inhibit PF-PC synaptic transmission by regulating the release of glutamate. G-protein-dependent cAMP-PKA signaling pathway may be involved in this process.

Structure, Function, and Pharmacology of Glutamate Receptor Ion Channels

Many physiologic effects of l-glutamate, the major excitatory neurotransmitter in the mammalian central nervous system, are mediated via signaling by ionotropic glutamate receptors (iGluRs). These ligand-gated ion channels are critical to brain function and are centrally implicated in numerous psychiatric and neurologic disorders. There are different classes of iGluRs with a variety of receptor subtypes in each class that play distinct roles in neuronal functions. The diversity in iGluR subtypes, with their unique functional properties and physiologic roles, has motivated a large number of studies. Our understanding of receptor subtypes has advanced considerably since the first iGluR subunit gene was cloned in 1989, and the research focus has expanded to encompass facets of biology that have been recently discovered and to exploit experimental paradigms made possible by technological advances. Here, we review insights from more than 3 decades of iGluR studies with an emphasis on the progress that has occurred in the past decade. We cover structure, function, pharmacology, roles in neurophysiology, and therapeutic implications for all classes of receptors assembled from the subunits encoded by the 18 ionotropic glutamate receptor genes. SIGNIFICANCE STATEMENT: Glutamate receptors play important roles in virtually all aspects of brain function and are either involved in mediating some clinical features of neurological disease or represent a therapeutic target for treatment. Therefore, understanding the structure, function, and pharmacology of this class of receptors will advance our understanding of many aspects of brain function at molecular, cellular, and system levels and provide new opportunities to treat patients.

Saturating Receiver and Receptor Competition in Synaptic DMC: Deterministic and Statistical Signal Models

Synaptic communication is based on a biological Molecular Communication (MC) system which may serve as a blueprint for the design of synthetic MC systems. However, the physical modeling of synaptic MC is complicated by the possible saturation of the molecular receiver caused by the competition of neurotransmitters (NTs) for postsynaptic receptors. Receiver saturation renders the system behavior nonlinear in the number of released NTs and is commonly neglected in existing analytical models. Furthermore, due to the ligands' competition for receptors (and vice versa), the individual binding events at the molecular receiver are in general not statistically independent and the commonly used binomial model for the statistics of the received signal does not apply. Hence, in this work, we propose a novel deterministic model for receptor saturation in terms of a state-space description based on an eigenfunction expansion of Fick's diffusion equation. The presented solution is numerically stable and computationally efficient. Employing the proposed deterministic model, we show that saturation at the molecular receiver effectively reduces the peak-value of the expected received signal and accelerates the clearance of NTs as compared to the case when receptor occupancy is neglected. We further derive a statistical model for the received signal in terms of the hypergeometric distribution which accounts for the competition of NTs for receptors and the competition of receptors for NTs. The proposed statistical model reveals how the signal statistics are shaped by the number of released NTs, the number of receptors, and the binding kinetics of the receptors, respectively, in the presence of competition. In particular, we show that the impact of these parameters on the signal variance is qualitatively different depending on the relative numbers of NTs and receptors. Finally, the accuracy of the proposed deterministic and statistical models is verified by particle-based computer simulations.

Dendritic spine geometry and spine apparatus organization govern the spatiotemporal dynamics of calcium

Dendritic spines are small subcompartments that protrude from the dendrites of neurons and are important for signaling activity and synaptic communication. These subcompartments have been characterized to have different shapes. While it is known that these shapes are associated with spine function, the specific nature of these shape-function relationships is not well understood. In this work, we systematically investigated the relationship between the shape and size of both the spine head and spine apparatus, a specialized endoplasmic reticulum compartment within the spine head, in modulating rapid calcium dynamics using mathematical modeling. We developed a spatial multicompartment reaction-diffusion model of calcium dynamics in three dimensions with various flux sources, including N-methyl-D-aspartate receptors (NMDARs), voltage-sensitive calcium channels (VSCCs), and different ion pumps on the plasma membrane. Using this model, we make several important predictions. First, the volume to surface area ratio of the spine regulates calcium dynamics. Second, membrane fluxes impact calcium dynamics temporally and spatially in a nonlinear fashion. Finally, the spine apparatus can act as a physical buffer for calcium by acting as a sink and rescaling the calcium concentration. These predictions set the stage for future experimental investigations of calcium dynamics in dendritic spines.

Switching On Depression and Potentiation in the Cerebellum

Long-term depression (LTD) and long-term potentiation (LTP) in the cerebellum are important for motor learning. However, the signaling mechanisms controlling whether LTD or LTP is induced in response to synaptic stimulation remain obscure. Using a unified model of LTD and LTP at the cerebellar parallel fiber-Purkinje cell (PF-PC) synapse, we delineate the coordinated pre- and postsynaptic signaling that determines the direction of plasticity. We show that LTP is the default response to PF stimulation above a well-defined frequency threshold. However, if the calcium signal surpasses the threshold for CaMKII activation, then an ultrasensitive "on switch" activates an extracellular signal-regulated kinase (ERK)-based positive feedback loop that triggers LTD instead. This postsynaptic feedback loop is sustained by another, trans-synaptic, feedback loop that maintains nitric oxide production throughout LTD induction. When full depression is achieved, an automatic "off switch" inactivates the feedback loops, returning the network to its basal state and demarcating the end of the early phase of LTD.

Postsynaptic Stability and Variability Described by a Stochastic Model of Endosomal Trafficking

Neurons undergo dynamic processes of constitutive AMPA-type glutamate receptor (AMPAR) trafficking, such as the insertion and internalization of AMPARs by exocytosis and endocytosis, while stably maintaining synaptic efficacy. Studies using advanced imaging techniques have suggested that the frequency of these constitutive trafficking processes, as well as the number of AMPARs that are involved in a particular event highly fluctuate. In addition, mechanisms that trigger some forms of synaptic plasticity have been shown to include not only these processes but also additional fluctuating processes, such as the sorting of AMPARs to late endosomes (LEs). Thus, the regulation of postsynaptic AMPARs by the endosomal trafficking system appears to have superficially conflicting properties between the stability or organized control of plasticity and highly fluctuating or stochastic processes. However, it is not clear how the endosomal trafficking system reconciles and utilizes such conflicting properties. Although deterministic models have been effective to describe the stable maintenance of synaptic AMPAR numbers by constitutive recycling, as well as the involvement of endosomal trafficking in synaptic plasticity, they do not take stochasticity into account. In this study, we introduced the stochasticity into the model of each crucial machinery of the endosomal trafficking system. The specific questions we solved by our improved model are whether stability is accomplished even with a combination of fluctuating processes, and how overall variability occurs while controlling long-term synaptic depression (LTD). Our new stochastic model indeed demonstrated the stable regulation of postsynaptic AMPAR numbers at the basal state and during LTD maintenance, despite fast fluctuations in AMPAR numbers as well as high variability in the time course and amounts of LTD. In addition, our analysis suggested that the high variability arising from this stochasticity is beneficial for reproducing the relatively constant timing of LE sorting for LTD. We therefore propose that the coexistence of stability and stochasticity in the endosomal trafficking system is suitable for stable synaptic transmission and the reliable induction of synaptic plasticity, with variable properties that have been observed experimentally.

From membrane receptors to protein synthesis and actin cytoskeleton: Mechanisms underlying long lasting forms of synaptic plasticity

Synaptic plasticity, the activity dependent change in synaptic strength, forms the molecular foundation of learning and memory. Synaptic plasticity includes structural changes, with spines changing their size to accomodate insertion and removal of postynaptic receptors, which are correlated with functional changes. Of particular relevance for memory storage are the long lasting forms of synaptic plasticity which are protein synthesis dependent. Due to the importance of spine structural plasticity and protein synthesis, this review focuses on the signaling pathways that connect synaptic stimulation with regulation of protein synthesis and remodeling of the actin cytoskeleton. We also review computational models that implement novel aspects of molecular signaling in synaptic plasticity, such as the role of neuromodulators and spatial microdomains, as well as highlight the need for computational models that connect activation of memory kinases with spine actin dynamics.

Ca2+ Requirements for Long-Term Depression Are Frequency Sensitive in Purkinje Cells

Cerebellar long-term depression (LTD) is a form of synaptic plasticity dependent on postsynaptic Ca²⁺ changes. One fundamental question is how LTD is selectively induced by specific numbers of Ca²⁺ pulses and which are the frequency and duration of this train of pulses required for LTD induction. The molecular mechanism which leads the integration of postsynaptic Ca²⁺ pulses in the LTD signaling network has not been elucidated either. Recent publications have shown that Ca²⁺/calmodulin-dependent protein kinase II (CaMKII) is required for LTD induction. Additionally, protein kinase C (PKC), CaMKII, and MAPK play an important role to transduce the frequency of Ca²⁺ pulses into their enzymatic activity levels; however, it is still unknown which enzymes are involved in decoding Ca²⁺ pulses in LTD. We have extended a stochastic model of LTD by adding the molecular network regulating CaMKII activity and its activation. We solved this model with stochastic engine for pathway simulation to include the effect of biochemical noise in LTD. We systematically investigated the dependence of LTD induction on stimulus frequencies, and we found that LTD is selectively induced by a specific number of Ca²⁺ spikes at different frequencies. We observed that CaMKII is essential to induce LTD, and LTD is only weakly induced when its Thr286 phosphorylation site has been deleted. We found that CaMKII decodes the frequency of Ca²⁺ spikes into different amounts of kinase activity during LTD induction. In addition, PKC and ERK enzyme activity is highly sensitive to the frequency and the number of Ca²⁺ pulses and this sensitivity has an important effect on LTD activation. This research predicts the postsynaptic Ca²⁺ requirements to induce LTD using a typical synaptic activation sequence and explains how LTD is selectively induced by specific number of Ca²⁺ pulses at different frequencies.

Integrative meta-modeling identifies endocytic vesicles, late endosome and the nucleus as the cellular compartments primarily directing RTK signaling

Recently, intracellular receptor signaling has been identified as a key component mediating cell responses for various receptor tyrosine kinases (RTKs). However, the extent each endocytic compartment (endocytic vesicle, early endosome, recycling endosome, late endosome, lysosome and nucleus) contributes to receptor signaling has not been quantified. Furthermore, our understanding of endocytosis and receptor signaling is complicated by cell- or receptor-specific endocytosis mechanisms. Therefore, towards understanding the differential endocytic compartment signaling roles, and identifying how to achieve signal transduction control for RTKs, we delineate how endocytosis regulates RTK signaling. We achieve this via a meta-analysis across eight RTKs, integrating computational modeling with experimentally derived cell (compartment volume, trafficking kinetics and pH) and ligand-receptor (ligand/receptor concentration and interaction kinetics) physiology. Our simulations predict the abundance of signaling from eight RTKs, identifying the following hierarchy in RTK signaling: PDGFRβ > IGFR1 > EGFR > PDGFRα > VEGFR1 > VEGFR2 > Tie2 > FGFR1. We find that endocytic vesicles are the primary cell signaling compartment; over 43% of total receptor signaling occurs within the endocytic vesicle compartment for these eight RTKs. Mechanistically, we found that high RTK signaling within endocytic vesicles may be attributed to their low volume (5.3 × 10^-19 L) which facilitates an enriched ligand concentration (3.2 μM per ligand molecule within the endocytic vesicle). Under the analyzed physiological conditions, we identified extracellular ligand concentration as the most sensitive parameter to change; hence the most significant one to modify when regulating absolute compartment signaling. We also found that the late endosome and nucleus compartments are important contributors to receptor signaling, where 26% and 18%, respectively, of average receptor signaling occurs across the eight RTKs. Conversely, we found very low membrane-based receptor signaling, exhibiting <1% of the total receptor signaling for these eight RTKs. Moreover, we found that nuclear translocation, mechanistically, requires late endosomal transport; when we blocked receptor trafficking from late endosomes to the nucleus we found a 57% reduction in nuclear translocation. In summary, our research has elucidated the significance of endocytic vesicles, late endosomes and the nucleus in RTK signal propagation.

A Model of Induction of Cerebellar Long-Term Depression Including RKIP Inactivation of Raf and MEK

We report an updated stochastic model of cerebellar Long Term Depression (LTD) with improved realism. Firstly, we verify experimentally that dissociation of Raf kinase inhibitor protein (RKIP) from Mitogen-activated protein kinase kinase (MEK) is required for cerebellar LTD and add this interaction to an earlier published model, along with the known requirement of dissociation of RKIP from Raf kinase. We update Ca²⁺ dynamics as a constant-rate influx, which captures experimental input profiles accurately. We improve α-amino-3-hydroxy-5-methyl-4 isoxazolepropionic acid (AMPA) receptor interactions by adding phosphorylation and dephosphorylation of AMPA receptors when bound to glutamate receptor interacting protein (GRIP). The updated model is tuned to reproduce experimental Ca²⁺ peak vs. LTD amplitude curves at four different Ca²⁺ pulse durations as closely as possible. We find that the updated model is generally more robust with these changes, yet we still observe some sensitivity of LTD induction to copy number of the key signaling molecule Protein kinase C (PKC). We predict natural variability in this number by stochastic diffusion may influence the probabilistic LTD response to Ca²⁺ input in Purkinje cell spines and propose this as an extra source of stochasticity that may be important also in other signaling systems.

A GluD Coming-Of-Age Story

The GluD1 and GluD2 receptors form the GluD ionotropic glutamate receptor (iGluR) subfamily. Without known endogenous ligands, they have long been referred to as 'orphan' and remained enigmatic functionally. Recent progress has, however, radically changed this view. Both GluD receptors are expressed in wider brain regions than originally thought. Human genetic studies and analyses of knockout mice have revealed their involvement in multiple neurodevelopmental and psychiatric disorders. The discovery of endogenous ligands, together with structural investigations, has opened the way towards a mechanistic understanding of GluD signaling at central nervous system synapses. These studies have also prompted the hypothesis that all iGluRs, and potentially other neurotransmitter receptors, rely on the cooperative binding of extracellular small-molecule and protein ligands for physiological signaling.