The role of dendritic spine morphology in the compartmentalization and delivery of surface receptors

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.

Trafficking proteins show limited differences in mobility across different postsynaptic spines

The function of the postsynaptic compartment is based on the presence and activity of postsynaptic receptors, whose dynamics are controlled by numerous scaffolding, signaling and trafficking proteins. Although the receptors and the scaffolding proteins have received substantial attention, the trafficking proteins have not been investigated extensively. Their mobility rates are unknown, and it is unclear how the postsynaptic environment affects their dynamics. To address this, we analyzed several trafficking proteins (α-synuclein, amphiphysin, calmodulin, doc2a, dynamin, and endophilin), estimating their movement rates in the dendritic shaft, as well as in morphologically distinct "mushroom" and "stubby" postsynapse types. The diffusion parameters were surprisingly similar across dendritic compartments, and a few differences between proteins became evident only in the presence of a synapse neck. We conclude that the movement of trafficking proteins is not strongly affected by the postsynaptic compartment, in stark contrast to the presynapse, which regulates strongly the movement of such proteins.

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.

Control of Ca2+ signals by astrocyte nanoscale morphology at tripartite synapses

Much of the Ca2+ activity in astrocytes is spatially restricted to microdomains and occurs in fine processes that form a complex anatomical meshwork, the so-called spongiform domain. A growing body of literature indicates that those astrocytic Ca2+ signals can influence the activity of neuronal synapses and thus tune the flow of information through neuronal circuits. Because of technical difficulties in accessing the small spatial scale involved, the role of astrocyte morphology on Ca2+ microdomain activity remains poorly understood. Here, we use computational tools and idealized 3D geometries of fine processes based on recent super-resolution microscopy data to investigate the mechanistic link between astrocytic nanoscale morphology and local Ca2+ activity. Simulations demonstrate that the nano-morphology of astrocytic processes powerfully shapes the spatio-temporal properties of Ca2+ signals and promotes local Ca2+ activity. The model predicts that this effect is attenuated upon astrocytic swelling, hallmark of brain diseases, which we confirm experimentally in hypo-osmotic conditions. Upon repeated neurotransmitter release events, the model predicts that swelling hinders astrocytic signal propagation. Overall, this study highlights the influence of the complex morphology of astrocytes at the nanoscale and its remodeling in pathological conditions on neuron-astrocyte communication at so-called tripartite synapses, where astrocytic processes come into close contact with pre- and postsynaptic structures.

Protein drift-diffusion dynamics and phase separation in curved cell membranes and dendritic spines: Hybrid discrete-continuum methods

We develop methods for investigating protein drift-diffusion dynamics in heterogeneous cell membranes and the roles played by geometry, diffusion, chemical kinetics, and phase separation. Our hybrid stochastic numerical methods combine discrete particle descriptions with continuum-level models for tracking the individual protein drift-diffusion dynamics when coupled to continuum fields. We show how our approaches can be used to investigate phenomena motivated by protein kinetics within dendritic spines. The spine geometry is hypothesized to play an important biological role regulating synaptic strength, protein kinetics, and self-assembly of clusters. We perform simulation studies for model spine geometries varying the neck size to investigate how phase-separation and protein organization is influenced by different shapes. We also show how our methods can be used to study the roles of geometry in reaction-diffusion systems including Turing instabilities. Our methods provide general approaches for investigating protein kinetics and drift-diffusion dynamics within curved membrane structures.

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.

The role of molecular diffusion within dendritic spines in synaptic function

Spines are tiny nanoscale protrusions from dendrites of neurons. In the cortex and hippocampus, most of the excitatory postsynaptic sites reside in spines. The bulbous spine head is connected to the dendritic shaft by a thin membranous neck. Because the neck is narrow, spine heads are thought to function as biochemically independent signaling compartments. Thus, dynamic changes in the composition, distribution, mobility, conformations, and signaling properties of molecules contained within spines can account for much of the molecular basis of postsynaptic function and regulation. A major factor in controlling these changes is the diffusional properties of proteins within this small compartment. Advances in measurement techniques using fluorescence microscopy now make it possible to measure molecular diffusion within single dendritic spines directly. Here, we review the regulatory mechanisms of diffusion in spines by local intra-spine architecture and discuss their implications for neuronal signaling and synaptic plasticity.

Ankyrins: Roles in synaptic biology and pathology

Ankyrins are broadly expressed adaptors that organize diverse membrane proteins into specialized domains and link them to the sub-membranous cytoskeleton. In neurons, ankyrins are known to have essential roles in organizing the axon initial segment and nodes of Ranvier. However, recent studies have revealed novel functions for ankyrins at synapses, where they organize and stabilize neurotransmitter receptors, modulate dendritic spine morphology and control adhesion to the presynaptic site. Ankyrin genes have also been highly associated with a range of neurodevelopmental and psychiatric diseases, including bipolar disorder, schizophrenia and autism, which all demonstrate overlap in their genetics, mechanisms and phenotypes. This review discusses the novel synaptic functions of ankyrin proteins in neurons, and places these exciting findings in the context of ANK genes as key neuropsychiatric disorder risk-factors.

Probing the Interplay between Dendritic Spine Morphology and Membrane-Bound Diffusion

Dendritic spines are protrusions along neuronal dendrites that harbor the majority of excitatory postsynapses. Their distinct morphology, often featuring a bulbous head and small neck that connects to the dendritic shaft, has been shown to facilitate compartmentalization of electrical and cytoplasmic signaling stimuli elicited at the synapse. The extent to which spine morphology also forms a barrier for membrane-bound diffusion has remained unclear. Recent simulations suggested that especially the diameter of the spine neck plays a limiting role in this process. Here, we examine the connection between spine morphology and membrane-bound diffusion through a combination of photoconversion, live-cell superresolution experiments, and numerical simulations. Local photoconversion was used to obtain the timescale of diffusive equilibration in spines and followed by global sparse photoconversion to determine spine morphologies with nanoscopic resolution. These morphologies were subsequently used to assess the role of morphology on the diffusive equilibration. From the simulations, we could determine a robust relation between the equilibration timescale and a generalized shape factor calculated using both spine neck width and neck length, as well as spine head size. Experimentally, we found that diffusive equilibration was often slower, but rarely faster than predicted from the simulations, indicating that other biological confounders further reduce membrane-bound diffusion in these spines. This shape-dependent membrane-bound diffusion in mature spines may contribute to spine-specific compartmentalization of neurotransmitter receptors and signaling molecules and thereby support long-term plasticity of synaptic contacts.

Protein Crowding within the Postsynaptic Density Can Impede the Escape of Membrane Proteins

Mechanisms regulating lateral diffusion and positioning of glutamate receptors within the postsynaptic density (PSD) determine excitatory synaptic strength. Scaffold proteins in the PSD are abundant receptor binding partners, yet electron microscopy suggests that the PSD is highly crowded, potentially restricting the diffusion of receptors regardless of binding. However, the contribution of macromolecular crowding to receptor retention remains poorly understood. We combined experimental and computational approaches to test the effect of synaptic crowding on receptor movement and positioning in Sprague Dawley rat hippocampal neurons. We modeled AMPA receptor diffusion in synapses where the distribution of scaffold proteins was determined from photoactivated localization microscopy experiments, and receptor-scaffold association and dissociation rates were adjusted to fit single-molecule tracking and fluorescence recovery measurements. Simulations predicted that variation of receptor size strongly influences the fractional synaptic area the receptor may traverse, and the proportion that may exchange in and out of the synapse. To test the model experimentally, we designed a set of novel transmembrane (TM) probes. A single-pass TM protein with one PDZ binding motif concentrated in the synapse as do AMPARs yet was more mobile there than the much larger AMPAR. Furthermore, either the single binding motif or an increase in cytoplasmic bulk through addition of a single GFP slowed synaptic movement of a small TM protein. These results suggest that both crowding and binding limit escape of AMPARs from the synapse. Moreover, tight protein packing within the PSD may modulate the synaptic dwell time of many TM proteins important for synaptic function.

SIGNIFICANCE STATEMENT

Small alterations to the distribution within synapses of key transmembrane proteins, such as receptors, can dramatically change synaptic strength. Indeed, many diseases are thought to unbalance neural circuit function in this manner. Processes that regulate this in healthy synapses are unclear, however. By combining computer simulations with imaging methods that examined protein dynamics at multiple scales in space and time, we showed that both steric effects and protein-protein binding each regulate the mobility of receptors in the synapse. Our findings extend our knowledge of the synapse as a crowded environment that counteracts molecular diffusion, and support the idea that both molecular collisions and biochemical binding can be involved in the regulation of neural circuit performance.

The Role of Synaptopodin in Membrane Protein Diffusion in the Dendritic Spine Neck

The dynamic exchange of neurotransmitter receptors at synapses relies on their lateral diffusion in the plasma membrane. At synapses located on dendritic spines this process is limited by the geometry of the spine neck that restricts the passage of membrane proteins. Biochemical compartmentalisation of the spine is believed to underlie the input-specificity of excitatory synapses and to set the scale on which functional changes can occur. Synaptopodin is located predominantly in the neck of dendritic spines, and is thus ideally placed to regulate the exchange of synaptic membrane proteins. The central aim of our study was to assess whether the presence of synaptopodin influences the mobility of membrane proteins in the spine neck and to characterise whether this was due to direct molecular interactions or to spatial constraints that are related to the structural organisation of the neck. Using single particle tracking we have identified a specific effect of synaptopodin on the diffusion of metabotropic mGluR5 receptors in the spine neck. However, super-resolution STORM/PALM imaging showed that this was not due to direct interactions between the two proteins, but that the presence of synaptopodin is associated with an altered local organisation of the F-actin cytoskeleton, that in turn could restrict the diffusion of membrane proteins with large intracellular domains through the spine neck. This study contributes new data on the way in which the spine neck compartmentalises excitatory synapses. Our data complement models that consider the impact of the spine neck as a function of its shape, by showing that the internal organisation of the neck imposes additional physical barriers to membrane protein diffusion.

Tracking the activity-dependent diffusion of synaptic proteins using restricted photoconversion of Dendra2

Spines are small protrusions on dendritic membranes receiving inputs from axonal termini. They consist in a head connected to the dendritic shaft by a narrow neck and contain multiple synaptic proteins that interact in a coordinated manner to allow for synaptic communication. This process involves many proteins that are moving in and out spines. However, comparing this synaptodendritic movement in basal and stimulated conditions is very challenging. Here we describe an elegant method to measure the activity-dependent diffusion of synaptic proteins using Dendra2 photoconversion. We provide a successful method to obtain Dendra2-photoconverted images and a step-by-step procedure to analyze the data. This live-imaging approach may also apply to investigate the diffusion of proteins across other subcellular compartments or organelles including but not restricted to, nucleus, nucleolus, ER, or vesicular structures. Once the imaging system is set up, data can be acquired in 1-30 min and analyzed in approximately 1-4 h.

Psychiatric risk factor ANK3/ankyrin-G nanodomains regulate the structure and function of glutamatergic synapses

Recent evidence implicates glutamatergic synapses as key pathogenic sites in psychiatric disorders. Common and rare variants in the ANK3 gene, encoding ankyrin-G, have been associated with bipolar disorder, schizophrenia, and autism. Here we demonstrate that ankyrin-G is integral to AMPAR-mediated synaptic transmission and maintenance of spine morphology. Using superresolution microscopy we find that ankyrin-G forms distinct nanodomain structures within the spine head and neck. At these sites, it modulates mushroom spine structure and function, probably as a perisynaptic scaffold and barrier within the spine neck. Neuronal activity promotes ankyrin-G accumulation in distinct spine subdomains, where it differentially regulates NMDA receptor-dependent plasticity. These data implicate subsynaptic nanodomains containing a major psychiatric risk molecule, ankyrin-G, as having location-specific functions and open directions for basic and translational investigation of psychiatric risk molecules.