Unified quantitative model of AMPA receptor trafficking at synapses

The interaction between KIF21A and KANK1 regulates dendritic morphology and synapse plasticity in neurons

JOURNAL/nrgr/04.03/01300535-202501000-00029/figure1/v/2024-05-14T021156Z/r/image-tiff Morphological alterations in dendritic spines have been linked to changes in functional communication between neurons that affect learning and memory. Kinesin-4 KIF21A helps organize the microtubule-actin network at the cell cortex by interacting with KANK1; however, whether KIF21A modulates dendritic structure and function in neurons remains unknown. In this study, we found that KIF21A was distributed in a subset of dendritic spines, and that these KIF21A-positive spines were larger and more structurally plastic than KIF21A-negative spines. Furthermore, the interaction between KIF21A and KANK1 was found to be critical for dendritic spine morphogenesis and synaptic plasticity. Knockdown of either KIF21A or KANK1 inhibited dendritic spine morphogenesis and dendritic branching, and these deficits were fully rescued by coexpressing full-length KIF21A or KANK1, but not by proteins with mutations disrupting direct binding between KIF21A and KANK1 or binding between KANK1 and talin1. Knocking down KIF21A in the hippocampus of rats inhibited the amplitudes of long-term potentiation induced by high-frequency stimulation and negatively impacted the animals' cognitive abilities. Taken together, our findings demonstrate the function of KIF21A in modulating spine morphology and provide insight into its role in synaptic function.

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.

Neuroligin-1 dependent phosphotyrosine signaling in excitatory synapse differentiation

Introduction

The synaptic adhesion molecule neuroligin-1 (NLGN1) is involved in the differentiation of excitatory synapses, but the precise underlying molecular mechanisms are still debated. Here, we explored the role of NLGN1 tyrosine phosphorylation in this process, focusing on a subset of receptor tyrosine kinases (RTKs), namely FGFR1 and Trks, that were previously described to phosphorylate NLGN1 at a unique intracellular residue (Y782).

Methods

We used pharmacological inhibitors and genetic manipulation of those RTKs in dissociated hippocampal neurons, followed by biochemical measurement of NLGN1 phosphorylation and immunocytochemical staining of excitatory synaptic scaffolds.

Results

This study shows that: (i) the accumulation of PSD-95 at de novo NLGN1 clusters induced by neurexin crosslinking is reduced by FGFR and Trk inhibitors; (ii) the increase in PSD-95 puncta caused by NLGN1 over-expression is impaired by FGFR and Trk inhibitors; (iii) TrkB activation by BDNF increases NLGN1 phosphorylation; and (iv) TrkB knock-down impairs the increase of PSD-95 puncta caused by NLGN1 over-expression, an effect which is not seen with the NLGN1 Y782A mutant.

Discussion

Together, our data identify TrkB as one of the major RTKs responsible for NLGN1 tyrosine phosphorylation, and reveal that TrkB activity is necessary for the synaptogenic effects of NLGN1.

Asymptotic analysis of particle cluster formation in the presence of anchoring sites

The aggregation or clustering of proteins and other macromolecules plays an important role in the formation of large-scale molecular assemblies within cell membranes. Examples of such assemblies include lipid rafts, and postsynaptic domains (PSDs) at excitatory and inhibitory synapses in neurons. PSDs are rich in scaffolding proteins that can transiently trap transmembrane neurotransmitter receptors, thus localizing them at specific spatial positions. Hence, PSDs play a key role in determining the strength of synaptic connections and their regulation during learning and memory. Recently, a two-dimensional (2D) diffusion-mediated aggregation model of PSD formation has been developed in which the spatial locations of the clusters are determined by a set of fixed anchoring sites. The system is kept out of equilibrium by the recycling of particles between the cell membrane and interior. This results in a stationary distribution consisting of multiple clusters, whose average size can be determined using an effective mean-field description of the particle concentration around each anchored cluster. In this paper, we derive corrections to the mean-field approximation by applying the theory of diffusion in singularly perturbed domains. The latter is a powerful analytical method for solving two-dimensional (2D) and three-dimensional (3D) diffusion problems in domains where small holes or perforations have been removed from the interior. Applications range from modeling intracellular diffusion, where interior holes could represent subcellular structures such as organelles or biological condensates, to tracking the spread of chemical pollutants or heat from localized sources. In this paper, we take the bounded domain to be the cell membrane and the holes to represent anchored clusters. The analysis proceeds by partitioning the membrane into a set of inner regions around each cluster, and an outer region where mean-field interactions occur. Asymptotically matching the inner and outer stationary solutions generates an asymptotic expansion of the particle concentration, which includes higher-order corrections to mean-field theory that depend on the positions of the clusters and the boundary of the domain. Motivated by a recent study of light-activated protein oligomerization in cells, we also develop the analogous theory for cluster formation in a three-dimensional (3D) domain. The details of the asymptotic analysis differ from the 2D case due to the contrasting singularity structure of 2D and 3D Green's functions.

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.

An abundance of free regulatory (19S) proteasome particles regulates neuronal synapses

The proteasome, the major protein-degradation machine in cells, regulates neuronal synapses and long-term information storage. Here, using super-resolution microscopy, we found that the two essential subcomplexes of the proteasome, the regulatory (19S) and catalytic (20S) particles, are differentially distributed within individual rat cortical neurons. We discovered an unexpected abundance of free 19S particles near synapses. The free neuronal 19S particles bind and deubiquitylate lysine 63-ubiquitin (Lys⁶³-ub), a non-proteasome-targeting ubiquitin linkage. Pull-down assays revealed a significant overrepresentation of synaptic molecules as Lys⁶³-ub interactors. Inhibition of the 19S deubiquitylase activity significantly altered excitatory synaptic transmission and reduced the synaptic availability of AMPA receptors at multiple trafficking points in a proteasome-independent manner. Together, these results reveal a moonlighting function of the regulatory proteasomal subcomplex near synapses.

Synaptic logistics: Competing over shared resources

High turnover rates of synaptic proteins imply that synapses constantly need to replace their constituent building blocks. This requires sophisticated supply chains and potentially exposes synapses to shortages as they compete for limited resources. Interestingly, competition in neurons has been observed at different scales. Whether it is competition of receptors for binding sites inside a single synapse or synapses fighting for resources to grow. Here we review the implications of such competition for synaptic function and plasticity. We identify multiple mechanisms that synapses use to safeguard themselves against supply shortages and identify a fundamental neurologistic trade-off governing the sizes of reserve pools of essential synaptic building blocks.

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.

Computational insights into mRNA and protein dynamics underlying synaptic plasticity rules

Recent advances in experimental techniques provide an unprecedented peek into the intricate molecular dynamics inside synapses and dendrites. The experimental insights into the molecular turnover revealed that such processes as diffusion, active transport, spine uptake, and local protein synthesis could dynamically modulate the copy numbers of plasticity-related molecules in synapses. Subsequently, theoretical models were designed to understand the interaction of these processes better and to explain how local synaptic plasticity cues can up or down-regulate the molecular copy numbers across synapses. In this review, we discuss the recent advances in experimental techniques and computational models to highlight how these complementary approaches can provide insight into molecular cross-talk across synapses, ultimately allowing us to develop biologically-inspired neural network models to understand brain function.

Quantifying postsynaptic receptor dynamics: insights into synaptic function

The molecular composition of presynaptic and postsynaptic neuronal terminals is dynamic, and yet long-term stabilizations in postsynaptic responses are necessary for synaptic development and long-term plasticity. The need to reconcile these concepts is further complicated by learning- and memory-related plastic changes in the molecular make-up of synapses. Advances in single-particle tracking mean that we can now quantify the number and diffusive properties of specific synaptic molecules, while statistical thermodynamics provides a framework to analyse these molecular fluctuations. In this Review, we discuss the use of these approaches to gain quantitative descriptions of the processes underlying the turnover, long-term stability and plasticity of postsynaptic receptors and show how these can help us to understand the balance between local molecular turnover and synaptic structural identity and integrity.

Spectral theory of diffusion in partially absorbing media

A probabilistic framework for studying single-particle diffusion in partially absorbing media has recently been developed in terms of an encounter-based approach. The latter computes the joint probability density (generalized propagator) for particle position X t and a Brownian functional U t that specifies the amount of time the particle is in contact with a reactive component M . Absorption occurs as soon as U t crosses a randomly distributed threshold (stopping time). Laplace transforming the propagator with respect to U t leads to a classical boundary value problem (BVP) in which the reactive component has a constant rate of absorption z , where z is the corresponding Laplace variable. Hence, a crucial step in the encounter-based approach is finding the inverse Laplace transform. In the case of a reactive boundary ∂ M , this can be achieved by solving a classical Robin BVP in terms of the spectral decomposition of a Dirichlet-to-Neumann (D-to-N) operator on ∂ M . In this paper, we develop the analogous construction in the case of a reactive substrate M . In particular, we show that the Laplace transformed propagator can be computed in terms of the spectral decomposition of a pair of D-to-N operators on ∂ M . However, inverting the Laplace transform with respect to z is considerably more involved. We illustrate the theory by considering the D-to-N operators for some simple geometries.

High-resolution imaging and manipulation of endogenous AMPA receptor surface mobility during synaptic plasticity and learning

Regulation of synaptic neurotransmitter receptor content is a fundamental mechanism for tuning synaptic efficacy during experience-dependent plasticity and behavioral adaptation. However, experimental approaches to track and modify receptor movements in integrated experimental systems are limited. Exploiting AMPA-type glutamate receptors (AMPARs) as a model, we generated a knock-in mouse expressing the biotin acceptor peptide (AP) tag on the GluA2 extracellular N-terminal. Cell-specific introduction of biotin ligase allows the use of monovalent or tetravalent avidin variants to respectively monitor or manipulate the surface mobility of endogenous AMPAR containing biotinylated AP-GluA2 in neuronal subsets. AMPAR immobilization precluded the expression of long-term potentiation and formation of contextual fear memory, allowing target-specific control of the expression of synaptic plasticity and animal behavior. The AP tag knock-in model offers unprecedented access to resolve and control the spatiotemporal dynamics of endogenous receptors, and opens new avenues to study the molecular mechanisms of synaptic plasticity and learning.

miR ‐124‐dependent tagging of synapses by synaptopodin enables input‐specific homeostatic plasticity

Homeostatic synaptic plasticity is a process by which neurons adjust their synaptic strength to compensate for perturbations in neuronal activity. Whether the highly diverse synapses on a neuron respond uniformly to the same perturbation remains unclear. Moreover, the molecular determinants that underlie synapse‐specific homeostatic synaptic plasticity are unknown. Here, we report a synaptic tagging mechanism in which the ability of individual synapses to increase their strength in response to activity deprivation depends on the local expression of the spine‐apparatus protein synaptopodin under the regulation of miR‐124. Using genetic manipulations to alter synaptopodin expression or regulation by miR‐124, we show that synaptopodin behaves as a “postsynaptic tag” whose translation is derepressed in a subpopulation of synapses and allows for nonuniform homeostatic strengthening and synaptic AMPA receptor stabilization. By genetically silencing individual connections in pairs of neurons, we demonstrate that this process operates in an input‐specific manner. Overall, our study shifts the current view that homeostatic synaptic plasticity affects all synapses uniformly to a more complex paradigm where the ability of individual synapses to undergo homeostatic changes depends on their own functional and biochemical state.

Local accumulation times in a diffusion-trapping model of receptor dynamics at proximal axodendritic synapses

The lateral diffusion and trapping of neurotransmitter receptors within the postsynaptic membrane of a neuron play a key role in determining synaptic strength and plasticity. Trapping is mediated by the reversible binding of receptors to scaffolding proteins (slots) within a synapse. In this paper we introduce a method for analyzing the transient dynamics of proximal axodendritic synapses in a diffusion-trapping model of receptor trafficking. Given a population of spatially distributed synapses, each of which has a fixed number of slots, we calculate the rate of relaxation to the steady-state distribution of bound slots (synaptic weights) in terms of a set of local accumulation times. Assuming that the rates of exocytosis and endocytosis are sufficiently slow, we show that the steady-state synaptic weights are independent of each other (purely local). On the other hand, the local accumulation time of a given synapse depends on the number of slots and the spatial location of all the synapses, indicating a form of transient heterosynaptic plasticity. This suggests that local accumulation time measurements could provide useful information regarding the distribution of synaptic weights within a dendrite.

MDGAs are fast-diffusing molecules that delay excitatory synapse development by altering neuroligin behavior

MDGA molecules can bind neuroligins and interfere with trans-synaptic interactions to neurexins, thereby impairing synapse development. However, the subcellular localization and dynamics of MDGAs, or their specific action mode in neurons remain unclear. Here, surface immunostaining of endogenous MDGAs and single molecule tracking of recombinant MDGAs in dissociated hippocampal neurons reveal that MDGAs are homogeneously distributed and exhibit fast membrane diffusion, with a small reduction in mobility across neuronal maturation. Knocking-down/out MDGAs using shRNAs and CRISPR/Cas9 strategies increases the density of excitatory synapses, the membrane confinement of neuroligin-1, and the phosphotyrosine level of neuroligins associated with excitatory post-synaptic differentiation. Finally, MDGA silencing reduces the mobility of AMPA receptors, increases the frequency of miniature EPSCs (but not IPSCs), and selectively enhances evoked AMPA-receptor-mediated EPSCs in CA1 pyramidal neurons. Overall, our results support a mechanism by which interactions between MDGAs and neuroligin-1 delays the assembly of functional excitatory synapses containing AMPA receptors.

High-Resolution Fluorescence Imaging Combined With Computer Simulations to Quantitate Surface Dynamics and Nanoscale Organization of Neuroligin-1 at Synapses

Neuroligins (NLGNs) form a family of cell adhesion molecules implicated in synapse development, but the mechanisms that retain these proteins at synapses are still incompletely understood. Recent studies indicate that surface-associated NLGN1 is diffusionally trapped at synapses, where it interacts with quasi-static scaffolding elements of the post-synaptic density. Whereas single molecule tracking reveals rapid diffusion and transient immobilization of NLGN1 at synapses within seconds, fluorescence recovery after photobleaching experiments indicate instead a long-term turnover of NLGN1 at synapse, in the hour time range. To gain insight into the mechanisms supporting NLGN1 anchorage at post-synapses and try to reconcile those experimental paradigms, we quantitatively analyzed here live-cell and super-resolution imaging experiments performed on NLGN1 using a newly released simulator of membrane protein dynamics for fluorescence microscopy, FluoSim. Based on a small set of parameters including diffusion coefficients, binding constants, and photophysical rates, the framework describes fairly well the dynamic behavior of extra-synaptic and synaptic NLGN1 over both short and long time ranges, and provides an estimate of NLGN1 copy numbers in post-synaptic densities at steady-state (around 50 dimers). One striking result is that the residence time of NLGN1 at synapses is much longer than what can be expected from extracellular interactions with pre-synaptic neurexins only, suggesting that NLGN1 is stabilized at synapses through multivalent interactions with intracellular post-synaptic scaffolding proteins.

Local accumulation time for diffusion in cells with gap junction coupling

In this paper we analyze the relaxation to steady state of intracellular diffusion in a pair of cells with gap-junction coupling. Gap junctions are prevalent in most animal organs and tissues, providing a direct diffusion pathway for both electrical and chemical communication between cells. Most analytical models of gap junctions focus on the steady-state diffusive flux and the associated effective diffusivity. Here we investigate the relaxation to steady state in terms of the so-called local accumulation time. The latter is commonly used to estimate the time to form a protein concentration gradient during morphogenesis. The basic idea is to treat the fractional deviation from the steady-state concentration as a cumulative distribution for the local accumulation time. One of the useful features of the local accumulation time is that it takes into account the fact that different spatial regions can relax at different rates. We consider both static and dynamic gap junction models. The former treats the gap junction as a resistive channel with effective permeability μ, whereas the latter represents the gap junction as a stochastic gate that randomly switches between an open and closed state. The local accumulation time is calculated by solving the diffusion equation in Laplace space and then taking the small-s limit. We show that the accumulation time is a monotonically increasing function of spatial position, with a jump discontinuity at the gap junction. This discontinuity vanishes in the limit μ→∞ for a static junction and β→0 for a stochastically gated junction, where β is the rate at which the gate closes. Finally, our results are generalized to the case of a linear array of cells with nearest-neighbor gap junction coupling.

Membrane trafficking and positioning of mGluRs at presynaptic and postsynaptic sites of excitatory synapses

The plethora of functions of glutamate in the brain are mediated by the complementary actions of ionotropic and metabotropic glutamate receptors (mGluRs). The ionotropic glutamate receptors carry most of the fast excitatory transmission, while mGluRs modulate transmission on longer timescales by triggering multiple intracellular signaling pathways. As such, mGluRs mediate critical aspects of synaptic transmission and plasticity. Interestingly, at synapses, mGluRs operate at both sides of the cleft, and thus bidirectionally exert the effects of glutamate. At postsynaptic sites, group I mGluRs act to modulate excitability and plasticity. At presynaptic sites, group II and III mGluRs act as auto-receptors, modulating release properties in an activity-dependent manner. Thus, synaptic mGluRs are essential signal integrators that functionally couple presynaptic and postsynaptic mechanisms of transmission and plasticity. Understanding how these receptors reach the membrane and are positioned relative to the presynaptic glutamate release site are therefore important aspects of synapse biology. In this review, we will discuss the currently known mechanisms underlying the trafficking and positioning of mGluRs at and around synapses, and how these mechanisms contribute to synaptic functioning. We will highlight outstanding questions and present an outlook on how recent technological developments will move this exciting research field forward.

Role of regulatory C-terminal motifs in synaptic confinement of LRRTM2

Leucine Rich Repeat Transmembrane proteins (LRRTMs) are neuronal cell adhesion molecules involved in synapse development and plasticity. LRRTM2 is the most synaptogenic isoform of the family, and its expression is strongly restricted to excitatory synapses in mature neurons. However, the mechanisms by which LRRTM2 is trafficked and stabilized at synapses remain unknown. Here, we examine the role of LRRTM2 intracellular domain on its membrane expression and stabilization at excitatory synapses, using a knock-down strategy combined to single molecule tracking and super-resolution dSTORM microscopy. We show that LRRTM2 operates an important shift in mobility after synaptogenesis in hippocampal neurons. Knock-down of LRRTM2 during synapse formation reduced excitatory synapse density in mature neurons. Deletion of LRRTM2 C-terminal domain abolished the compartmentalization of LRRTM2 in dendrites and disrupted its synaptic enrichment. Furtheremore, we show that LRRTM2 diffusion is increased in the absence of its intracellular domain, and that the protein is more dispersed at synapses. Surprisingly, LRRTM2 confinement at synapses was strongly dependent on a YxxC motif in the C-terminal domain, but was independent of the PDZ-like binding motif ECEV. Finally, the nanoscale organization of LRRTM2 at excitatory synapses depended on its C-terminal domain, with involvement of both the PDZ-binding and YxxC motifs. Altogether, these results demonstrate that LRRTM2 trafficking and enrichment at excitatory synapses are dependent on its intracellular domain.

Lack of support for surface diffusion of postsynaptic AMPARs in tuning synaptic transmission

Repetitive stimulation of excitatory synapses triggers molecular events required for signal transfer across neuronal synapses. It has been hypothesized that one of these molecular events, the diffusion of extrasynaptic α-amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid receptor (AMPARs) (i.e., the diffusion hypothesis), is necessary to help synapses recover from paired-pulse depression. To examine this presumed role of AMPAR diffusion during repetitive presynaptic stimulation, a biophysical model based on published physiological results was developed to track the localization and gating of each AMPAR. The model demonstrates that AMPAR gating in short intervals of fewer than 100 ms is controlled by their position in relation to the glutamate release site and by their recovery from desensitization, but it is negligibly influenced by their diffusion. Therefore, these simulations failed to demonstrate a role for AMPAR diffusion in helping synapses recover from paired-pulse depression.

The biophysical basis underlying the maintenance of early phase long-term potentiation

The maintenance of synaptic changes resulting from long-term potentiation (LTP) is essential for brain function such as memory and learning. Different LTP phases have been associated with diverse molecular processes and pathways, and the molecular underpinnings of LTP on the short, as well as long time scales, are well established. However, the principles on the intermediate time scale of 1-6 hours that mediate the early phase of LTP (E-LTP) remain elusive. We hypothesize that the interplay between specific features of postsynaptic receptor trafficking is responsible for sustaining synaptic changes during this LTP phase. We test this hypothesis by formalizing a biophysical model that integrates several experimentally-motivated mechanisms. The model captures a wide range of experimental findings and predicts that synaptic changes are preserved for hours when the receptor dynamics are shaped by the interplay of structural changes of the spine in conjunction with increased trafficking from recycling endosomes and the cooperative binding of receptors. Furthermore, our model provides several predictions to verify our findings experimentally.

FluoSim: simulator of single molecule dynamics for fluorescence live-cell and super-resolution imaging of membrane proteins

Fluorescence live-cell and super-resolution microscopy methods have considerably advanced our understanding of the dynamics and mesoscale organization of macro-molecular complexes that drive cellular functions. However, different imaging techniques can provide quite disparate information about protein motion and organization, owing to their respective experimental ranges and limitations. To address these issues, we present here a robust computer program, called FluoSim, which is an interactive simulator of membrane protein dynamics for live-cell imaging methods including SPT, FRAP, PAF, and FCS, and super-resolution imaging techniques such as PALM, dSTORM, and uPAINT. FluoSim integrates diffusion coefficients, binding rates, and fluorophore photo-physics to calculate in real time the localization and intensity of thousands of independent molecules in 2D cellular geometries, providing simulated data directly comparable to actual experiments. FluoSim was thoroughly validated against experimental data obtained on the canonical neurexin-neuroligin adhesion complex at cell-cell contacts. This unified software allows one to model and predict membrane protein dynamics and localization at the ensemble and single molecule level, so as to reconcile imaging paradigms and quantitatively characterize protein behavior in complex cellular environments.

Shank Proteins Couple the Endocytic Zone to the Postsynaptic Density to Control Trafficking and Signaling of Metabotropic Glutamate Receptor 5

Activation of postsynaptic metabotropic glutamate receptors (mGluRs) modulates neuronal excitability and synaptic plasticity, while deregulation of mGluR signaling has been implicated in neurodevelopmental disorders. Overstimulation of mGluRs is restricted by the rapid endocytosis of receptors after activation. However, how membrane trafficking of mGluRs at synapses is controlled remains poorly defined. We find that in hippocampal neurons, the agonist-induced receptor internalization of synaptic mGluR5 is significantly reduced in Shank knockdown neurons. This is rescued by the re-expression of wild-type Shanks, but not by mutants unable to bind Homer1b/c, Dynamin2, or Cortactin. These effects are paralleled by a reduction in synapses associated with an endocytic zone. Moreover, a mutation in SHANK2 found in autism spectrum disorders (ASDs) similarly disrupts these processes. On the basis of these findings, we propose that synaptic Shank scaffolds anchor the endocytic machinery to govern the efficient trafficking of mGluR5 and to balance the surface expression of mGluRs to efficiently modulate neuronal functioning.

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Receptor activation triggers efficient internalization of mGluR5 in spines

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Shank proteins control mGluR5 trafficking and signaling

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Shanks link essential components of the endocytic zone to the postsynaptic density

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Mutation in SHANK2 found in ASD disrupt these processes

Molecular Crowding and Diffusion-Capture in Synapses

Cell membranes often contain domains with important physiological functions. A typical example are neuronal synapses, whose capacity to capture receptors for neurotransmitters is central to neuronal functions. Receptors diffuse in the membrane until they are stabilized by interactions with stable elements, the scaffold. Single particle tracking experiments demonstrated that these interactions are rather weak and that lateral diffusion is strongly impaired in the post-synaptic membrane due to molecular crowding. We investigated how the distribution of scaffolding molecules and molecular crowding affect the capture of receptors. In particle-based Monte Carlo simulations, based on experimental data of molecular diffusion and organization, crowding enhanced the receptor-scaffold interaction but reduced the capture of new molecules. The distribution of scaffolding sites in several clusters reduced crowding and fostered the exchange of molecules accelerating synaptic plasticity. Synapses could switch between two regimes, becoming more stable or more plastic depending on the internal distribution of molecules.

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The good: molecular crowding enhances the interaction receptors-scaffold

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The bad: the exchange of molecules with extrasynaptic areas is reduced by crowding

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Molecular crowding helps synapses to be stable

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Nanoclusters of scaffold sites reduce crowding effects and favor synaptic plasticity

Optogenetic control of excitatory post-synaptic differentiation through neuroligin-1 tyrosine phosphorylation

Neuroligins (Nlgns) are adhesion proteins mediating trans-synaptic contacts in neurons. However, conflicting results around their role in synaptic differentiation arise from the various techniques used to manipulate Nlgn expression level. Orthogonally to these approaches, we triggered here the phosphorylation of endogenous Nlgn1 in CA1 mouse hippocampal neurons using a photoactivatable tyrosine kinase receptor (optoFGFR1). Light stimulation for 24 hr selectively increased dendritic spine density and AMPA-receptor-mediated EPSCs in wild-type neurons, but not in Nlgn1 knock-out neurons or when endogenous Nlgn1 was replaced by a non-phosphorylatable mutant (Y782F). Moreover, light stimulation of optoFGFR1 partially occluded LTP in a Nlgn1-dependent manner. Combined with computer simulations, our data support a model by which Nlgn1 tyrosine phosphorylation promotes the assembly of an excitatory post-synaptic scaffold that captures surface AMPA receptors. This optogenetic strategy highlights the impact of Nlgn1 intracellular signaling in synaptic differentiation and potentiation, while enabling an acute control of these mechanisms.

Pin1 Binding to Phosphorylated PSD-95 Regulates the Number of Functional Excitatory Synapses

The post-synaptic density protein 95 (PSD-95) plays a central role in excitatory synapse development and synaptic plasticity. Phosphorylation of the N-terminus of PSD-95 at threonine 19 (T19) and serine 25 (S25) decreases PSD-95 stability at synapses; however, a molecular mechanism linking PSD-95 phosphorylation to altered synaptic stability is lacking. Here, we show that phosphorylation of T19/S25 recruits the phosphorylation-dependent peptidyl-prolyl cis-trans isomerase (Pin1) and reduces the palmitoylation of Cysteine 3 and Cysteine 5 in PSD-95. This reduction in PSD-95 palmitoylation accounts for the observed loss in the number of dendritic PSD-95 clusters, the increased AMPAR mobility, and the decreased number of functional excitatory synapses. We find the effects of Pin1 overexpression were all rescued by manipulations aimed at increasing the levels of PSD-95 palmitoylation. Therefore, Pin1 is a key signaling molecule that regulates the stability of excitatory synapses and may participate in the destabilization of PSD-95 following the induction of synaptic plasticity.

Structure and plasticity of silent synapses in developing hippocampal neurons visualized by super-resolution imaging

Excitatory synapses in the mammalian brain exhibit diverse functional properties in transmission and plasticity. Directly visualizing the structural correlates of such functional heterogeneity is often hindered by the diffraction-limited resolution of conventional optical imaging techniques. Here, we used super-resolution stochastic optical reconstruction microscopy (STORM) to resolve structurally distinct excitatory synapses formed on dendritic shafts and spines. The majority of these shaft synapses contained N-methyl-d-aspartate receptors (NMDARs) but not α-amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid receptors (AMPARs), suggesting that they were functionally silent. During development, as more spine synapses formed with increasing sizes and expression of AMPARs and NMDARs, shaft synapses exhibited moderate reduction in density with largely unchanged sizes and receptor expression. Furthermore, upon glycine stimulation to induce chemical long-term potentiation (cLTP), the previously silent shaft synapses became functional shaft synapses by recruiting more AMPARs than did spine synapses. Thus, silent shaft synapse may represent a synaptic state in developing neurons with enhanced capacity of activity-dependent potentiation.

Vangl2 acts at the interface between actin and N-cadherin to modulate mammalian neuronal outgrowth

Dynamic mechanical interactions between adhesion complexes and the cytoskeleton are essential for axon outgrowth and guidance. Whether planar cell polarity (PCP) proteins, which regulate cytoskeleton dynamics and appear necessary for some axon guidance, also mediate interactions with membrane adhesion is still unclear. Here we show that Vangl2 controls growth cone velocity by regulating the internal retrograde actin flow in an N-cadherin-dependent fashion. Single molecule tracking experiments show that the loss of Vangl2 decreased fast-diffusing N-cadherin membrane molecules and increased confined N-cadherin trajectories. Using optically manipulated N-cadherin-coated microspheres, we correlated this behavior to a stronger mechanical coupling of N-cadherin with the actin cytoskeleton. Lastly, we show that the spatial distribution of Vangl2 within the growth cone is selectively affected by an N-cadherin-coated substrate. Altogether, our data show that Vangl2 acts as a negative regulator of axonal outgrowth by regulating the strength of the molecular clutch between N-cadherin and the actin cytoskeleton.

How mRNA Localization and Protein Synthesis Sites Influence Dendritic Protein Distribution and Dynamics

Proteins drive the function of neuronal synapses. The synapses are distributed throughout the dendritic arbor, often hundreds of micrometers away from the soma. It is still unclear how somatic and dendritic sources of proteins shape protein distribution and respectively contribute to local protein changes during synaptic plasticity. Here, we present a unique computational framework describing for a given protein species the dendritic distribution of the mRNA and the corresponding protein in a dendrite. Using CaMKIIα as a test case, our model reveals the key role active transport plays in the maintenance of dendritic mRNA and protein levels and predicts the short and long timescales of protein dynamics. Our model reveals the fundamental role of mRNA localization and dendritic mRNA translation in synaptic maintenance and plasticity in distal compartments. We developed a web application for neuroscientists to explore the dynamics of the mRNA or protein of interest.

Differential role of pre- and postsynaptic neurons in the activity-dependent control of synaptic strengths across dendrites

Neurons receive a large number of active synaptic inputs from their many presynaptic partners across their dendritic tree. However, little is known about how the strengths of individual synapses are controlled in balance with other synapses to effectively encode information while maintaining network homeostasis. This is in part due to the difficulty in assessing the activity of individual synapses with identified afferent and efferent connections for a synapse population in the brain. Here, to gain insights into the basic cellular rules that drive the activity-dependent spatial distribution of pre- and postsynaptic strengths across incoming axons and dendrites, we combine patch-clamp recordings with live-cell imaging of hippocampal pyramidal neurons in dissociated cultures and organotypic slices. Under basal conditions, both pre- and postsynaptic strengths cluster on single dendritic branches according to the identity of the presynaptic neurons, thus highlighting the ability of single dendritic branches to exhibit input specificity. Stimulating a single presynaptic neuron induces input-specific and dendritic branchwise spatial clustering of presynaptic strengths, which accompanies a widespread multiplicative scaling of postsynaptic strengths in dissociated cultures and heterosynaptic plasticity at distant synapses in organotypic slices. Our study provides evidence for a potential homeostatic mechanism by which the rapid changes in global or distant postsynaptic strengths compensate for input-specific presynaptic plasticity.

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.

Biophysical mechanisms underlying the membrane trafficking of synaptic adhesion molecules

Adhesion proteins play crucial roles at synapses, not only by providing a physical trans-synaptic linkage between axonal and dendritic membranes, but also by connecting to functional elements including the pre-synaptic neurotransmitter release machinery and post-synaptic receptors. To mediate these functions, adhesion proteins must be organized on the neuronal surface in a precise and controlled manner. Recent studies have started to describe the mobility, nanoscale organization, and turnover rate of key synaptic adhesion molecules including cadherins, neurexins, neuroligins, SynCAMs, and LRRTMs, and show that some of these proteins are highly mobile in the plasma membrane while others are confined at sub-synaptic compartments, providing evidence for different regulatory pathways. In this review article, we provide a biophysical view of the diffusional trapping of adhesion molecules at synapses, involving both extracellular and intracellular protein interactions. We review the methodology underlying these measurements, including biomimetic systems with purified adhesion proteins, means to perturb protein expression or function, single molecule imaging in cultured neurons, and analytical models to interpret the data. This article is part of the special issue entitled 'Mobility and trafficking of neuronal membrane proteins'.

The actions of volatile anesthetics: a new perspective

This article reviews recent work in applying neutron and X-ray scattering towards the elucidation of the molecular mechanisms of volatile anesthetics. Experimental results on domain mixing in ternary lipid mixtures, and the influence of volatile anesthetics and hydrostatic pressure are placed in the contexts of ion-channel function and receptor trafficking at the postsynaptic density.

Shank and Zinc Mediate an AMPA Receptor Subunit Switch in Developing Neurons

During development, pyramidal neurons undergo dynamic regulation of AMPA receptor (AMPAR) subunit composition and density to help drive synaptic plasticity and maturation. These normal developmental changes in AMPARs are particularly vulnerable to risk factors for Autism Spectrum Disorders (ASDs), which include loss or mutations of synaptic proteins and environmental insults, such as dietary zinc deficiency. Here, we show how Shank2 and Shank3 mediate a zinc-dependent regulation of AMPAR function and subunit switch from GluA2-lacking to GluA2-containing AMPARs. Over development, we found a concomitant increase in Shank2 and Shank3 with GluA2 at synapses, implicating these molecules as potential players in AMPAR maturation. Since Shank activation and function require zinc, we next studied whether neuronal activity regulated postsynaptic zinc at glutamatergic synapses. Zinc was found to increase transiently and reversibly with neuronal depolarization at synapses, which could affect Shank and AMPAR localization and activity. Elevated zinc induced multiple functional changes in AMPAR, indicative of a subunit switch. Specifically, zinc lengthened the decay time of AMPAR-mediated synaptic currents and reduced their inward rectification in young hippocampal neurons. Mechanistically, both Shank2 and Shank3 were necessary for the zinc-sensitive enhancement of AMPAR-mediated synaptic transmission and act in concert to promote removal of GluA1 while enhancing recruitment of GluA2 at pre-existing Shank puncta. These findings highlight a cooperative local dynamic regulation of AMPAR subunit switch controlled by zinc signaling through Shank2 and Shank3 to shape the biophysical properties of developing glutamatergic synapses. Given the zinc sensitivity of young neurons and its dependence on Shank2 and Shank3, genetic mutations and/or environmental insults during early development could impair synaptic maturation and circuit formation that underlie ASD etiology.

A unique intracellular tyrosine in neuroligin-1 regulates AMPA receptor recruitment during synapse differentiation and potentiation

To better understand the molecular mechanisms by which early neuronal connections mature into synapses, we examined the impact of neuroligin-1 (Nlg1) phosphorylation on synapse differentiation, focusing on a unique intracellular tyrosine (Y782), which differentially regulates Nlg1 binding to PSD-95 and gephyrin. By expressing Nlg1 point mutants (Y782A/F) in hippocampal neurons, we show using imaging and electrophysiology that Y782 modulates the recruitment of functional AMPA receptors (AMPARs). Nlg1-Y782F impaired both dendritic spine formation and AMPAR diffusional trapping, but not NMDA receptor recruitment, revealing the assembly of silent synapses. Furthermore, replacing endogenous Nlg1 with either Nlg1-Y782A or -Y782F in CA1 hippocampal neurons impaired long-term potentiation (LTP), demonstrating a critical role of AMPAR synaptic retention. Screening of tyrosine kinases combined with pharmacological inhibitors point to Trk family members as major regulators of endogenous Nlg1 phosphorylation and synaptogenic function. Thus, Nlg1 tyrosine phosphorylation signaling is a critical event in excitatory synapse differentiation and LTP.

Neuroligins are postsynaptic cell adhesion molecules thought to play roles in synaptic development and function. Here, authors show that phosphorylation of Y782 in neuroligin-1 modulates its role in differentiation and ability to recruit AMPARs including during long-term potentiation.

Competition for synaptic building blocks shapes synaptic plasticity

Changes in the efficacies of synapses are thought to be the neurobiological basis of learning and memory. The efficacy of a synapse depends on its current number of neurotransmitter receptors. Recent experiments have shown that these receptors are highly dynamic, moving back and forth between synapses on time scales of seconds and minutes. This suggests spontaneous fluctuations in synaptic efficacies and a competition of nearby synapses for available receptors. Here we propose a mathematical model of this competition of synapses for neurotransmitter receptors from a local dendritic pool. Using minimal assumptions, the model produces a fast multiplicative scaling behavior of synapses. Furthermore, the model explains a transient form of heterosynaptic plasticity and predicts that its amount is inversely related to the size of the local receptor pool. Overall, our model reveals logistical tradeoffs during the induction of synaptic plasticity due to the rapid exchange of neurotransmitter receptors between synapses.

Pre-post synaptic alignment through neuroligin-1 tunes synaptic transmission efficiency

The nanoscale organization of neurotransmitter receptors regarding pre-synaptic release sites is a fundamental determinant of the synaptic transmission amplitude and reliability. How modifications in the pre- and post-synaptic machinery alignments affects synaptic currents, has only been addressed with computer modelling. Using single molecule super-resolution microscopy, we found a strong spatial correlation between AMPA receptor (AMPAR) nanodomains and the post-synaptic adhesion protein neuroligin-1 (NLG1). Expression of a truncated form of NLG1 disrupted this correlation without affecting the intrinsic AMPAR organization, shifting the pre-synaptic release machinery away from AMPAR nanodomains. Electrophysiology in dissociated and organotypic hippocampal rodent cultures shows these treatments significantly decrease AMPAR-mediated miniature and EPSC amplitudes. Computer modelling predicts that ~100 nm lateral shift between AMPAR nanoclusters and glutamate release sites induces a significant reduction in AMPAR-mediated currents. Thus, our results suggest the synapses necessity to release glutamate precisely in front of AMPAR nanodomains, to maintain a high synaptic responses efficiency.

A Revised View on the Role of Surface AMPAR Mobility in Tuning Synaptic Transmission: Limitations, Tools, and Alternative Views

Calcium dynamics in presynaptic terminals regulate the response dynamics of most central excitatory synapses. However, this dogma has been challenged by the hypothesis that mobility of the postsynaptic alpha-amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid subtype glutamate receptors (AMPAR) plays a role in tuning fast excitatory synaptic transmission. In this review, we reevaluate the factors regulating postsynaptic AMPAR mobility, reassess the modeling parameters, analyze the experimental tools, and end by providing alternative ideas stemming from recent results. In particular, newer methods of labeling AMPARs with small fluorophores in live neurons, combined with super-resolution microscopy and sub-second dynamics, lends support to the idea that AMPARs are primarily within the synapse, are greatly constrained, and have much slower mobility than previously thought. We discuss new experiments which may be necessary to readdress the role of postsynaptic AMPAR mobility in tuning fast excitatory synaptic transmission.

AMPA receptor trafficking and its role in heterosynaptic plasticity

Historically, long-term potentiation (LTP) and long-term depression (LTD), the best-characterized forms of long-term synaptic plasticity, are viewed as experience-dependent and input-specific processes. However, cumulative experimental and theoretical data have demonstrated that LTP and LTD can promote compensatory alterations in non-stimulated synapses. In this work, we have developed a computational model of a tridimensional spiny dendritic segment to investigate the role of AMPA receptor (AMPAR) trafficking during synaptic plasticity at specific synapses and its consequences for the populations of AMPAR at nearby synapses. Our results demonstrated that the mechanisms of AMPAR trafficking involved with LTP and LTD can promote heterosynaptic plasticity at non-stimulated synapses. These alterations are compensatory and arise from molecular competition. Moreover, the heterosynaptic changes observed in our model can modulate further activity-driven inductions of synaptic plasticity.

Quantum dot conjugated nanobodies for multiplex imaging of protein dynamics at synapses

Neurons communicate with each other through synapses, which show enrichment for specialized receptors. Although many studies have explored spatial enrichment and diffusion of these receptors in dissociated neurons using single particle tracking, much less is known about their dynamic properties at synapses in complex tissue like brain slices. Here we report the use of smaller and highly specific quantum dots conjugated with a recombinant single domain antibody fragment (VHH fragment) against green fluorescent protein to provide information on diffusion of adhesion molecules at the growth cone and neurotransmitter receptors at synapses. Our data reveals that QD-nanobodies can measure neurotransmitter receptor dynamics at both excitatory and inhibitory synapses in primary neuronal cultures as well as in ex vivo rat brain slices. We also demonstrate that this approach can be applied to tagging multiple proteins to simultaneously monitor their behavior. Thus, we provide a strategy for multiplex imaging of tagged membrane proteins to study their clustering, diffusion and transport both in vitro as well as in native tissue environments such as brain slices.

Self-crowding of AMPA receptors in the excitatory postsynaptic density can effectuate anomalous receptor sub-diffusion

AMPA receptors (AMPARs) and their associations with auxiliary transmembrane proteins are bulky structures with large steric-exclusion volumes. Hence, self-crowding of AMPARs, depending on the local density, may affect their lateral diffusion in the postsynaptic membrane as well as in the highly crowded postsynaptic density (PSD) at excitatory synapses. Earlier theoretical studies considered only the roles of transmembrane obstacles and the AMPAR-binding submembranous scaffold proteins in shaping receptor diffusion within PSD. Using lattice model of diffusion, the present study investigates the additional impacts of self-crowding on the anomalousity and effective diffusion coefficient (D_eff) of AMPAR diffusion. A recursive algorithm for avoiding false self-blocking during diffusion simulation is also proposed. The findings suggest that high density of AMPARs in the obstacle-free membrane itself engenders strongly anomalous diffusion and severe decline in D_eff. Adding transmembrane obstacles to the membrane accentuates the anomalousity arising from self-crowding due to the reduced free diffusion space. Contrarily, enhanced AMPAR-scaffold binding, either through increase in binding strength or scaffold density or both, ameliorates the anomalousity resulting from self-crowding. However, binding has differential impacts on D_eff depending on the receptor density. Increase in binding causes consistent decrease in D_eff for low and moderate receptor density. For high density, binding increases D_eff as long as it reduces anomalousity associated with intense self-crowding. Given a sufficiently strong binding condition when diffusion acquires normal behavior, further increase in binding causes decrease in D_eff. Supporting earlier experimental observations are mentioned and implications of present findings to the experimental observations on AMPAR diffusion are also drawn.

The transmembrane AMPA receptors (AMPARs) prominently exhibit lateral diffusion in the postsynaptic membrane at excitatory synapses. Steric obstructions to AMPAR diffusion due to the crowd of other relatively static transmembrane proteins and binding of AMPARs to the submembranous scaffold proteins in the specialized region of postsynaptic density (PSD) are well known to retard receptor diffusion, which causes receptor trapping and accumulation within PSD. However, AMPARs are significantly bulky structures and may also obstruct their own diffusion paths in the presence of their high density. It is shown here that intense self-crowding of AMPARs may lead to highly obstructed and confined receptor diffusion even in the obstacle-free medium, and the presence of other obstacles further aggravates this effect. AMPAR-scaffold binding reduces confined diffusion arising from self-crowding and strong binding engenders normal diffusion even at high receptor density. However, it overall causes reduction in the effective diffusion coefficient of the receptor diffusion.

A Simple and Powerful Analysis of Lateral Subdiffusion Using Single Particle Tracking

In biological membranes, many factors such as cytoskeleton, lipid composition, crowding, and molecular interactions deviate lateral diffusion from the expected random walks. These factors have different effects on diffusion but act simultaneously, so the observed diffusion is a complex mixture of diffusive behaviors (directed, Brownian, anomalous, or confined). Therefore, commonly used approaches to quantify diffusion based on averaging of the displacements such as the mean square displacement, are not adapted to the analysis of this heterogeneity. We introduce a parameter-the packing coefficient Pc, which gives an estimate of the degree of free movement that a molecule displays in a period of time independently of its global diffusivity. Applying this approach to two different situations (diffusion of a lipid probe and trapping of receptors at synapses), we show that Pc detected and localized temporary changes of diffusive behavior both in time and in space. More importantly, it allowed the detection of periods with very high confinement as well as their frequency and duration, and thus it can be used to calculate the effective k_on and k_off of scaffolding interactions such as those that immobilize receptors at synapses.

The Nanoworld of the Tripartite Synapse: Insights from Super-Resolution Microscopy

Synaptic connections between individual nerve cells are fundamental to the process of information transfer and storage in the brain. Over the past decades a third key partner of the synaptic machinery has been unveiled: ultrathin processes of electrically passive astroglia which often surround pre- and postsynaptic structures. The recent advent of super-resolution (SR) microscopy has begun to uncover the dynamic nanoworld of synapses and their astroglial environment. Here we overview and discuss the current progress in our understanding of the synaptic nanoenvironment, as gleaned from the imaging methods that go beyond the diffraction limit of conventional light microscopy. We argue that such methods are essential to achieve a new level of comprehension pertinent to the principles of signal integration in the brain.

Electrodiffusion phenomena in neuroscience: a neglected companion

The emerging technological revolution in genetically encoded molecular sensors and super-resolution imaging provides neuroscientists with a pass to the real-time nano-world. On this small scale, however, classical principles of electrophysiology do not always apply. This is in large part because the nanoscopic heterogeneities in ionic concentrations and the local electric fields associated with individual ions and their movement can no longer be ignored. Here, we review basic principles of molecular electrodiffusion in the cellular environment of organized brain tissue. We argue that accurate interpretation of physiological observations on the nanoscale requires a better understanding of the underlying electrodiffusion phenomena.

Timely regulated sorting from early to late endosomes is required to maintain cerebellar long-term depression

An important feature of long-term synaptic plasticity is the prolonged maintenance of plastic changes in synaptic transmission. The trafficking of AMPA-type glutamate receptors (AMPARs) is involved in the expression of many forms of synaptic plasticity, yet the subsequent events accomplishing the maintenance of plastic changes in synaptic AMPAR numbers are not fully understood. Here, we find that maintenance of cerebellar long-term depression results from a reduction in the number of AMPARs residing within endocytic recycling pathways. We then develop a genetically encoded, photosensitive inhibitor of late endosome sorting and use this to discover that initial maintenance of long-term depression relies on timely regulated late endosome sorting, which exhibits a threshold as well as switch-like behavior. Thus, our results indicate that recycling AMPAR numbers are reduced by a switching machinery of transient late endosome sorting, and that this process enables the transition from basal synaptic transmission to long-term depression maintenance.

Long term depression (LTD) of the cerebellum is known to be mediated by postsynaptic trafficking of glutamate receptor AMPAR. Here, Kim and colleagues show that early- to late-endosomal sorting of AMPAR represents the switch from expression to maintenance phase of cerebellar LTD.

Distribution of randomly diffusing particles in inhomogeneous media

Diffusion can be conceptualized, at microscopic scales, as the random hopping of particles between neighboring lattice sites. In the case of diffusion in inhomogeneous media, distinct spatial domains in the system may yield distinct particle hopping rates. Starting from the master equations (MEs) governing diffusion in inhomogeneous media we derive here, for arbitrary spatial dimensions, the deterministic lattice equations (DLEs) specifying the average particle number at each lattice site for randomly diffusing particles in inhomogeneous media. We consider the case of free (Fickian) diffusion with no steric constraints on the maximum particle number per lattice site as well as the case of diffusion under steric constraints imposing a maximum particle concentration. We find, for both transient and asymptotic regimes, excellent agreement between the DLEs and kinetic Monte Carlo simulations of the MEs. The DLEs provide a computationally efficient method for predicting the (average) distribution of randomly diffusing particles in inhomogeneous media, with the number of DLEs associated with a given system being independent of the number of particles in the system. From the DLEs we obtain general analytic expressions for the steady-state particle distributions for free diffusion and, in special cases, diffusion under steric constraints in inhomogeneous media. We find that, in the steady state of the system, the average fraction of particles in a given domain is independent of most system properties, such as the arrangement and shape of domains, and only depends on the number of lattice sites in each domain, the particle hopping rates, the number of distinct particle species in the system, and the total number of particles of each particle species in the system. Our results provide general insights into the role of spatially inhomogeneous particle hopping rates in setting the particle distributions in inhomogeneous media.

Stochastic lattice model of synaptic membrane protein domains

Neurotransmitter receptor molecules, concentrated in synaptic membrane domains along with scaffolds and other kinds of proteins, are crucial for signal transmission across chemical synapses. In common with other membrane protein domains, synaptic domains are characterized by low protein copy numbers and protein crowding, with rapid stochastic turnover of individual molecules. We study here in detail a stochastic lattice model of the receptor-scaffold reaction-diffusion dynamics at synaptic domains that was found previously to capture, at the mean-field level, the self-assembly, stability, and characteristic size of synaptic domains observed in experiments. We show that our stochastic lattice model yields quantitative agreement with mean-field models of nonlinear diffusion in crowded membranes. Through a combination of analytic and numerical solutions of the master equation governing the reaction dynamics at synaptic domains, together with kinetic Monte Carlo simulations, we find substantial discrepancies between mean-field and stochastic models for the reaction dynamics at synaptic domains. Based on the reaction and diffusion properties of synaptic receptors and scaffolds suggested by previous experiments and mean-field calculations, we show that the stochastic reaction-diffusion dynamics of synaptic receptors and scaffolds provide a simple physical mechanism for collective fluctuations in synaptic domains, the molecular turnover observed at synaptic domains, key features of the observed single-molecule trajectories, and spatial heterogeneity in the effective rates at which receptors and scaffolds are recycled at the cell membrane. Our work sheds light on the physical mechanisms and principles linking the collective properties of membrane protein domains to the stochastic dynamics that rule their molecular components.

Stochastic Induction of Long-Term Potentiation and Long-Term Depression

Long-term depression (LTD) and long-term potentiation (LTP) of granule-Purkinje cell synapses are persistent synaptic alterations induced by high and low rises of the intracellular calcium ion concentration ([Ca²⁺]), respectively. The occurrence of LTD involves the activation of a positive feedback loop formed by protein kinase C, phospholipase A₂, and the extracellular signal-regulated protein kinase pathway, and its expression comprises the reduction of the population of synaptic AMPA receptors. Recently, a stochastic computational model of these signalling processes demonstrated that, in single synapses, LTD is probabilistic and bistable. Here, we expanded this model to simulate LTP, which requires protein phosphatases and the increase in the population of synaptic AMPA receptors. Our results indicated that, in single synapses, while LTD is bistable, LTP is gradual. Ca²⁺ induced both processes stochastically. The magnitudes of the Ca²⁺ signals and the states of the signalling network regulated the likelihood of LTP and LTD and defined dynamic macroscopic Ca²⁺ thresholds for the synaptic modifications in populations of synapses according to an inverse Bienenstock, Cooper and Munro (BCM) rule or a sigmoidal function. In conclusion, our model presents a unifying mechanism that explains the macroscopic properties of LTP and LTD from their dynamics in single synapses.