Properties of Quantal Transmission at CA1 Synapses

Signatures of Bayesian inference emerge from energy-efficient synapses

Biological synaptic transmission is unreliable, and this unreliability likely degrades neural circuit performance. While there are biophysical mechanisms that can increase reliability, for instance by increasing vesicle release probability, these mechanisms cost energy. We examined four such mechanisms along with the associated scaling of the energetic costs. We then embedded these energetic costs for reliability in artificial neural networks (ANNs) with trainable stochastic synapses, and trained these networks on standard image classification tasks. The resulting networks revealed a tradeoff between circuit performance and the energetic cost of synaptic reliability. Additionally, the optimised networks exhibited two testable predictions consistent with pre-existing experimental data. Specifically, synapses with lower variability tended to have (1) higher input firing rates and (2) lower learning rates. Surprisingly, these predictions also arise when synapse statistics are inferred through Bayesian inference. Indeed, we were able to find a formal, theoretical link between the performance-reliability cost tradeoff and Bayesian inference. This connection suggests two incompatible possibilities: evolution may have chanced upon a scheme for implementing Bayesian inference by optimising energy efficiency, or alternatively, energy-efficient synapses may display signatures of Bayesian inference without actually using Bayes to reason about uncertainty.

Fusion pore flux controls the rise-times of quantal synaptic responses

The release of neurotransmitter from a single synaptic vesicle generates a quantal response, which at excitatory synapses in voltage-clamped neurons is referred to as a miniature excitatory postsynaptic current (mEPSC). We analyzed mEPSCs in cultured mouse hippocampal neurons and in HEK cells expressing postsynaptic proteins enabling them to receive synaptic inputs from cocultured neurons. mEPSC amplitudes and rise-times varied widely within and between cells. In neurons, mEPSCs with larger amplitudes had longer rise-times, and this correlation was stronger in neurons with longer mean rise-times. In HEK cells, this correlation was weak and unclear. Standard mechanisms thought to govern mEPSCs cannot account for these results. We therefore developed models to simulate mEPSCs and assess their dependence on different factors. Modeling indicated that longer diffusion times for transmitters released by larger vesicles to reach more distal receptors cannot account for the correlation between rise-time and amplitude. By contrast, incorporating the vesicle size dependence of fusion pore expulsion time recapitulated experimental results well. Larger vesicles produce mEPSCs with larger amplitudes and also take more time to lose their content. Thus, fusion pore flux directly contributes to mEPSC rise-time. Variations in fusion pores account for differences among neurons, between neurons and HEK cells, and the correlation between rise-time and the slope of rise-time versus amplitude plots. Plots of mEPSC amplitude versus rise-time are sensitive to otherwise inaccessible properties of a synapse and offer investigators a means of assessing the role of fusion pores in synaptic release.

Activity-dependent diffusion trapping of AMPA receptors as a key step for expression of early LTP

This review focuses on the activity-dependent diffusion trapping of α-amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid receptors (AMPARs) as a crucial mechanism for the expression of early long-term potentiation (LTP), a process central to learning and memory. Despite decades of research, the precise mechanisms by which LTP induction leads to an increase in AMPAR responses at synapses have been elusive. We review the different hypotheses that have been put forward to explain the increased AMPAR responsiveness during LTP. We discuss the dynamic nature of AMPAR complexes, including their constant turnover and activity-dependent modifications that affect their synaptic accumulation. We highlight a hypothesis suggesting that AMPARs are diffusively trapped at synapses through activity-dependent interactions with protein-based binding slots in the post-synaptic density (PSD), offering a potential explanation for the increased synaptic strength during LTP. Furthermore, we outline the challenges still to be addressed before we fully understand the functional roles and molecular mechanisms of AMPAR dynamic nanoscale organization in LTP. This article is part of a discussion meeting issue 'Long-term potentiation: 50 years on'.

Nanoscale architecture of synaptic vesicles and scaffolding complexes revealed by cryo-electron tomography

The spatial distribution of proteins and their arrangement within the cellular ultrastructure regulates the opening of α-amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid (AMPA) receptors in response to glutamate release at the synapse. Fluorescence microscopy imaging revealed that the postsynaptic density (PSD) and scaffolding proteins in the presynaptic active zone (AZ) align across the synapse to form a trans-synaptic "nanocolumn," but the relation to synaptic vesicle release sites is uncertain. Here, we employ focused-ion beam (FIB) milling and cryoelectron tomography to image synapses under near-native conditions. Improved image contrast, enabled by FIB milling, allows simultaneous visualization of supramolecular nanoclusters within the AZ and PSD and synaptic vesicles. Surprisingly, membrane-proximal synaptic vesicles, which fuse to release glutamate, are not preferentially aligned with AZ or PSD nanoclusters. These synaptic vesicles are linked to the membrane by peripheral protein densities, often consistent in size and shape with Munc13, as well as globular densities bridging the synaptic vesicle and plasma membrane, consistent with prefusion complexes of SNAREs, synaptotagmins, and complexin. Monte Carlo simulations of synaptic transmission events using biorealistic models guided by our tomograms predict that clustering AMPARs within PSD nanoclusters increases the variability of the postsynaptic response but not its average amplitude. Together, our data support a model in which synaptic strength is tuned at the level of single vesicles by the spatial relationship between scaffolding nanoclusters and single synaptic vesicle fusion sites.

Tuning synaptic strength by regulation of AMPA glutamate receptor localization

Long-term potentiation (LTP) of excitatory synapses is a leading model to explain the concept of information storage in the brain. Multiple mechanisms contribute to LTP, but central amongst them is an increased sensitivity of the postsynaptic membrane to neurotransmitter release. This sensitivity is predominantly determined by the abundance and localization of AMPA-type glutamate receptors (AMPARs). A combination of AMPAR structural data, super-resolution imaging of excitatory synapses, and an abundance of electrophysiological studies are providing an ever-clearer picture of how AMPARs are recruited and organized at synaptic junctions. Here, we review the latest insights into this process, and discuss how both cytoplasmic and extracellular receptor elements cooperate to tune the AMPAR response at the hippocampal CA1 synapse.

Structural and functional reorganization of inhibitory synapses by activity-dependent cleavage of neuroligin-2

Recent evidence has demonstrated that the transsynaptic nanoscale organization of synaptic proteins plays a crucial role in regulating synaptic strength in excitatory synapses. However, the molecular mechanism underlying this transsynaptic nanostructure in inhibitory synapses still remains unclear and its impact on synapse function in physiological or pathological contexts has not been demonstrated. In this study, we utilized an engineered proteolysis technique to investigate the effects of acute cleavage of neuroligin-2 (NL2) on synaptic transmission. Our results show that the rapid cleavage of NL2 led to impaired synaptic transmission by reducing both neurotransmitter release probability and quantum size. These changes were attributed to the dispersion of RIM1/2 and GABAA receptors and a weakened spatial alignment between them at the subsynaptic scale, as observed through superresolution imaging and model simulations. Importantly, we found that endogenous NL2 undergoes rapid MMP9-dependent cleavage during epileptic activities, which further exacerbates the decrease in inhibitory transmission. Overall, our study demonstrates the significant impact of nanoscale structural reorganization on inhibitory transmission and unveils ongoing modulation of mature GABAergic synapses through active cleavage of NL2 in response to hyperactivity.

Trans-synaptic molecular context of NMDA receptor nanodomains

Tight coordination of the spatial relationships between protein complexes is required for cellular function. In neuronal synapses, many proteins responsible for neurotransmission organize into subsynaptic nanoclusters whose trans-cellular alignment modulates synaptic signal propagation. However, the spatial relationships between these proteins and NMDA receptors (NMDARs), which are required for learning and memory, remain undefined. Here, we mapped the relationship of key NMDAR subunits to reference proteins in the active zone and postsynaptic density using multiplexed super-resolution DNA-PAINT microscopy. GluN2A and GluN2B subunits formed nanoclusters with diverse configurations that, surprisingly, were not localized near presynaptic vesicle release sites marked by Munc13-1. However, a subset of presynaptic sites was configured to maintain NMDAR activation: these were internally denser, aligned with abundant PSD-95, and associated closely with specific NMDAR nanodomains. This work reveals a new principle regulating NMDAR signaling and suggests that synaptic functional architecture depends on assembly of multiprotein nanodomains whose interior construction is conditional on trans-cellular relationships.

Acute reorganization of postsynaptic GABAA receptors reveals the functional impact of molecular nanoarchitecture at inhibitory synapses

Neurotransmitter receptors partition into nanometer-scale subdomains within the postsynaptic membrane that are precisely aligned with presynaptic neurotransmitter release sites. While spatial coordination between pre- and postsynaptic elements is observed at both excitatory and inhibitory synapses, the functional significance of this molecular architecture has been challenging to evaluate experimentally. Here we utilized an optogenetic clustering approach to acutely alter the nanoscale organization of the postsynaptic inhibitory scaffold gephyrin while monitoring synaptic function. Gephyrin clustering rapidly enlarged postsynaptic area, laterally displacing GABAA receptors from their normally precise apposition with presynaptic active zones. Receptor displacement was accompanied by decreased synaptic GABAA receptor currents even though presynaptic release probability and the overall abundance and function of synaptic GABAA receptors remained unperturbed. Thus, acutely repositioning neurotransmitter receptors within the postsynaptic membrane profoundly influences synaptic efficacy, establishing the functional importance of precision pre-/postsynaptic molecular coordination at inhibitory synapses.

Modification of the synaptic cleft under excitatory conditions

The synaptic cleft is the extracellular part of the synapse, bridging the pre- and postsynaptic membranes. The geometry and molecular organization of the cleft is gaining increased attention as an important determinant of synaptic efficacy. The present study by electron microscopy focuses on short-term morphological changes at the synaptic cleft under excitatory conditions. Depolarization of cultured hippocampal neurons with high K+ results in an increased frequency of synaptic profiles with clefts widened at the periphery (open clefts), typically exhibiting patches of membranes lined by postsynaptic density, but lacking associated presynaptic membranes (18.0% open clefts in high K+ compared to 1.8% in controls). Similarly, higher frequencies of open clefts were observed in adult brain upon a delay of perfusion fixation to promote excitatory/ischemic conditions. Inhibition of basal activity in cultured neurons through the application of TTX results in the disappearance of open clefts whereas application of NMDA increases their frequency (19.0% in NMDA vs. 5.3% in control and 2.6% in APV). Depletion of extracellular Ca2+ with EGTA also promotes an increase in the frequency of open clefts (16.6% in EGTA vs. 4.0% in controls), comparable to that by depolarization or NMDA, implicating dissociation of Ca2+-dependent trans-synaptic bridges. Dissociation of transsynaptic bridges under excitatory conditions may allow perisynaptic mobile elements, such as AMPA receptors to enter the cleft. In addition, peripheral opening of the cleft would facilitate neurotransmitter clearance and thus may have a homeostatic and/or protective function.

Estimation of cumulative amplitude distributions of miniature postsynaptic currents allows characterising their multimodality, quantal size and variability

A miniature postsynaptic current (mPSC) is a small, rare, and highly variable spontaneous synaptic event that is generally caused by the spontaneous release of single vesicles. The amplitude and variability of mPSCs are key measures of the postsynaptic processes and are taken as the main characteristics of an elementary unit (quantal size) in traditional quantal analysis of synaptic transmission. Due to different sources of biological and measurement noise, recordings of mPSCs exhibit high trial-to-trial heterogeneity, and experimental measurements of mPSCs are usually noisy and scarce, making their analysis demanding. Here, we present a sequential procedure for precise analysis of mPSC amplitude distributions for the range of small currents. To illustrate the developed approach, we chose previously obtained experimental data on the effect of the extracellular matrix on synaptic plasticity. The proposed statistical technique allowed us to identify previously unnoticed additional modality in the mPSC amplitude distributions, indicating the formation of new immature synapses upon ECM attenuation. We show that our approach can reliably detect multimodality in the distributions of mPSC amplitude, allowing for accurate determination of the size and variability of the quantal synaptic response. Thus, the proposed method can significantly expand the informativeness of both existing and newly obtained experimental data. We also demonstrated that mPSC amplitudes around the threshold of microcurrent excitation follow the Gumbel distribution rather than the binomial statistics traditionally used for a wide range of currents, either for a single synapse or when taking into consideration small influences of the adjacent synapses. Such behaviour is argued to originate from the theory of extreme processes. Specifically, recorded mPSCs represent instant random current fluctuations, among which there are relatively larger spikes (extreme events). They required more level of coherence that can be provided by different mechanisms of network or system level activation including neuron circuit signalling and extrasynaptic processes.

Postsynaptic protein assembly in three and two dimensions studied by mesoscopic simulations

Recently, cellular biomolecular condensates formed via phase separation have received considerable attention. While they can be formed either in cytosol (denoted as 3D) or beneath the membrane (2D), the underlying difference between the two has not been well clarified. To compare the phase behaviors in 3D and 2D, postsynaptic density (PSD) serves as a model system. PSD is a protein condensate located under the postsynaptic membrane that influences the localization of glutamate receptors and thus contributes to synaptic plasticity. Recent in vitro studies have revealed the formation of droplets of various soluble PSD proteins via liquid-liquid phase separation. However, it is unclear how these protein condensates are formed beneath the membrane and how they specifically affect the localization of glutamate receptors in the membrane. In this study, focusing on the mixture of a glutamate receptor complex, AMPAR-TARP, and a ubiquitous scaffolding protein, PSD-95, we constructed a mesoscopic model of protein-domain interactions in PSD and performed comparative molecular simulations. The results showed a sharp contrast in the phase behaviors of protein assemblies in 3D and those under the membrane (2D). A mixture of a soluble variant of the AMPAR-TARP complex and PSD-95 in the 3D system resulted in a phase-separated condensate, which was consistent with the experimental results. However, with identical domain interactions, AMPAR-TARP embedded in the membrane formed clusters with PSD-95, but did not form a stable separated phase. Thus, the cluster formation behaviors of PSD proteins in the 3D and 2D systems were distinct. The current study suggests that, more generally, stable phase separation can be more difficult to achieve in and beneath the membrane than in 3D systems.

Neurexin-3 subsynaptic densities are spatially distinct from Neurexin-1 and essential for excitatory synapse nanoscale organization in the hippocampus

Proteins critical for synaptic transmission are non-uniformly distributed and assembled into regions of high density called subsynaptic densities (SSDs) that transsynaptically align in nanocolumns. Neurexin-1 and neurexin-3 are essential presynaptic adhesion molecules that non-redundantly control NMDAR- and AMPAR-mediated synaptic transmission, respectively, via transsynaptic interactions with distinct postsynaptic ligands. Despite their functional relevance, fundamental questions regarding the nanoscale properties of individual neurexins, their influence on the subsynaptic organization of excitatory synapses and the mechanisms controlling how individual neurexins engage in precise transsynaptic interactions are unknown. Using Double Helix 3D dSTORM and neurexin mouse models, we identify neurexin-3 as a critical presynaptic adhesion molecule that regulates excitatory synapse nano-organization in hippocampus. Furthermore, endogenous neurexin-1 and neurexin-3 form discrete and non-overlapping SSDs that are enriched opposite their postsynaptic ligands. Thus, the nanoscale organization of neurexin-1 and neurexin-3 may explain how individual neurexins signal in parallel to govern different synaptic properties.

Plasticity of postsynaptic nanostructure

The postsynaptic density (PSD) of excitatory synapses is built from a wide variety of scaffolding proteins, receptors, and signaling molecules that collectively orchestrate synaptic transmission. Seminal work over the past decades has led to the identification and functional characterization of many PSD components. In contrast, we know far less about how these constituents are assembled within synapses, and how this organization contributes to synapse function. Notably, recent evidence from high-resolution microscopy studies and in silico models, highlights the importance of the precise subsynaptic structure of the PSD for controlling the strength of synaptic transmission. Even further, activity-driven changes in the distribution of glutamate receptors are acknowledged to contribute to long-term changes in synaptic efficacy. Thus, defining the mechanisms that drive structural changes within the PSD are important for a molecular understanding of synaptic transmission and plasticity. Here, we review the current literature on how the PSD is organized to mediate basal synaptic transmission and how synaptic activity alters the nanoscale organization of synapses to sustain changes in synaptic strength.

Targeted sensors for glutamatergic neurotransmission

Optical report of neurotransmitter release allows visualisation of excitatory synaptic transmission. Sensitive genetically-encoded fluorescent glutamate reporters operating with a range of affinities and emission wavelengths are available. However, without targeting to synapses, the specificity of the fluorescent signal is uncertain, compared to sensors directed at vesicles or other synaptic markers. We fused the state-of-the-art reporter iGluSnFR to glutamate receptor auxiliary proteins in order to target it to postsynaptic sites. Chimeras of Stargazin and gamma-8 that we named SnFR-γ2 and SnFR-γ8, were enriched at synapses, retained function and reported spontaneous glutamate release in rat hippocampal cells, with apparently diffraction-limited spatial precision. In autaptic mouse neurons cultured on astrocytic microislands, evoked neurotransmitter release could be quantitatively detected at tens of synapses in a field of view whilst evoked currents were recorded simultaneously. These experiments revealed a specific postsynaptic deficit from Stargazin overexpression, resulting in synapses with normal neurotransmitter release but without postsynaptic responses. This defect was reverted by delaying overexpression. By working at different calcium concentrations, we determined that SnFR-γ2 is a linear reporter of the global quantal parameters and short-term synaptic plasticity, whereas iGluSnFR is not. On average, half of iGluSnFR regions of interest (ROIs) showing evoked fluorescence changes had intense rundown, whereas less than 5% of SnFR-γ2 ROIs did. We provide an open-source analysis suite for extracting quantal parameters including release probability from fluorescence time series of individual and grouped synaptic responses. Taken together, postsynaptic targeting improves several properties of iGluSnFR and further demonstrates the importance of subcellular targeting for optogenetic actuators and reporters.

Computational modeling of trans-synaptic nanocolumns, a modulator of synaptic transmission

Understanding synaptic transmission is of crucial importance in neuroscience. The spatial organization of receptors, vesicle release properties and neurotransmitter molecule diffusion can strongly influence features of synaptic currents. Newly discovered structures coined trans-synaptic nanocolumns were shown to align presynaptic vesicles release sites and postsynaptic receptors. However, how these structures, spanning a few tens of nanometers, shape synaptic signaling remains little understood. Given the difficulty to probe submicroscopic structures experimentally, computer modeling is a useful approach to investigate the possible functional impacts and role of nanocolumns. In our in silico model, as has been experimentally observed, a nanocolumn is characterized by a tight distribution of postsynaptic receptors aligned with the presynaptic vesicle release site and by the presence of trans-synaptic molecules which can modulate neurotransmitter molecule diffusion. In this work, we found that nanocolumns can play an important role in reinforcing synaptic current mostly when the presynaptic vesicle contains a small number of neurotransmitter molecules. Our work proposes a new methodology to investigate in silico how the existence of trans-synaptic nanocolumns, the nanometric organization of the synapse and the lateral diffusion of receptors shape the features of the synaptic current such as its amplitude and kinetics.

Neuroligin-3 confines AMPA receptors into nanoclusters, thereby controlling synaptic strength at the calyx of Held synapses

The subsynaptic organization of postsynaptic neurotransmitter receptors into nanoclusters that are aligned with presynaptic release sites is essential for the high fidelity of synaptic transmission. However, the mechanisms controlling the nanoscale organization of neurotransmitter receptors in vivo remain incompletely understood. Here, we deconstructed the role of neuroligin-3 (Nlgn3), a postsynaptic adhesion molecule linked to autism, in organizing AMPA-type glutamate receptors in the calyx of Held synapse. Deletion of Nlgn3 lowered the amplitude and slowed the kinetics of AMPA receptor-mediated synaptic responses. Super-resolution microscopy revealed that, unexpectedly, these impairments in synaptic transmission were associated with an increase in the size of postsynaptic PSD-95 and AMPA receptor nanoclusters but a decrease of the densities in these clusters. Modeling showed that a dilution of AMPA receptors into larger nanocluster volumes decreases synaptic strength. Nlgn3, likely by binding to presynaptic neurexins, thus is a key organizer of AMPA receptor nanoclusters that likely acts via PSD-95 adaptors to optimize the fidelity of synaptic transmission.

Correlative Assembly of Subsynaptic Nanoscale Organizations During Development

Nanoscale organization of presynaptic proteins determines the sites of transmitter release, and its alignment with assemblies of postsynaptic receptors through nanocolumns is suggested to optimize the efficiency of synaptic transmission. However, it remains unknown how these nano-organizations are formed during development. In this study, we used super-resolution stochastic optical reconstruction microscopy (STORM) imaging technique to systematically analyze the evolvement of subsynaptic organization of three key synaptic proteins, namely, RIM1/2, GluA1, and PSD-95, during synapse maturation in cultured hippocampal neurons. We found that volumes of synaptic clusters and their subsynaptic heterogeneity increase as synapses get matured. Synapse sizes of presynaptic and postsynaptic compartments correlated well at all stages, while only more mature synapses demonstrated a significant correlation between presynaptic and postsynaptic nano-organizations. After a long incubation with an inhibitor of action potentials or AMPA receptors, both presynaptic and postsynaptic compartments showed increased synaptic cluster volume and subsynaptic heterogeneity; however, the trans-synaptic alignment was intact. Together, our results characterize the evolvement of subsynaptic protein architectures during development and demonstrate that the nanocolumn is organized more likely by an intrinsic mechanism and independent of synaptic activities.

Nanoscale rules governing the organization of glutamate receptors in spine synapses are subunit specific

Heterotetrameric glutamate receptors are essential for the development, function, and plasticity of spine synapses but how they are organized to achieve this is not known. Here we show that the nanoscale organization of glutamate receptors containing specific subunits define distinct subsynaptic features. Glutamate receptors containing GluA2 or GluN1 subunits establish nanomodular elements precisely positioned relative to Synaptotagmin-1 positive presynaptic release sites that scale with spine size. Glutamate receptors containing GluA1 or GluN2B specify features that exhibit flexibility: GluA1-subunit containing AMPARs are found in larger spines, while GluN2B-subunit containing NMDARs are enriched in the smallest spines with neither following a strict modular organization. Given that the precise positioning of distinct classes of glutamate receptors is linked to diverse events including cell death and synaptic plasticity, this unexpectedly robust synaptic nanoarchitecture provides a resilient system, where nanopositioned glutamate receptor heterotetramers define specific subsynaptic regions of individual spine synapses.

Glutamate receptors comprise two obligate subunits and two subunits that confer distinct properties and functions to the specific tetramers, which also localize to distinct synaptic spines. Here, the authors use STimulated Emission Depletion nanoscopy (STED) to provide detailed insights into the spatial organization of glutamate receptor types.

Nano-Organization at the Synapse: Segregation of Distinct Forms of Neurotransmission

Synapses maintain synchronous, asynchronous, and spontaneous modes of neurotransmission through distinct molecular and biochemical pathways. Traditionally a single synapse was assumed to have a homogeneous organization of molecular components both at the active zone and post-synaptically. However, recent advancements in experimental tools and the further elucidation of the physiological significance of distinct forms of release have challenged this notion. In comparison to rapid evoked release, the physiological significance of both spontaneous and asynchronous neurotransmission has only recently been considered in parallel with synaptic structural organization. Active zone nanostructure aligns with postsynaptic nanostructure creating a precise trans-synaptic alignment of release sites and receptors shaping synaptic efficacy, determining neurotransmission reliability, and tuning plasticity. This review will discuss how studies delineating synaptic nanostructure create a picture of a molecularly heterogeneous active zone tuned to distinct forms of release that may dictate diverse synaptic functional outputs.

Heterogeneity of glutamatergic synapses: cellular mechanisms and network consequences

Chemical synapses are commonly known as a structurally and functionally highly diverse class of cell-cell contacts specialized to mediate communication between neurons. They represent the smallest "computational" unit of the brain and are typically divided into excitatory and inhibitory as well as modulatory categories. These categories are subdivided into diverse types, each representing a different structure-function repertoire that in turn are thought to endow neuronal networks with distinct computational properties. The diversity of structure and function found among a given category of synapses is referred to as heterogeneity. The main building blocks for this heterogeneity are synaptic vesicles, the active zone, the synaptic cleft, the postsynaptic density, and glial processes associated with the synapse. Each of these five structural modules entails a distinct repertoire of functions, and their combination specifies the range of functional heterogeneity at mammalian excitatory synapses, which are the focus of this review. We describe synapse heterogeneity that is manifested on different levels of complexity ranging from the cellular morphology of the pre- and postsynaptic cells toward the expression of different protein isoforms at individual release sites. We attempt to define the range of structural building blocks that are used to vary the basic functional repertoire of excitatory synaptic contacts and discuss sources and general mechanisms of synapse heterogeneity. Finally, we explore the possible impact of synapse heterogeneity on neuronal network function.

Deorphanization of novel biogenic amine-gated ion channels identifies a new serotonin receptor for learning

Pentameric ligand-gated ion channels (LGICs) play conserved, critical roles in both excitatory and inhibitory synaptic transmission and can be activated by diverse neurochemical ligands. We have performed a characterization of orphan channels from the nematode C. elegans, identifying five new monoamine-gated LGICs with diverse functional properties and expression postsynaptic to aminergic neurons. These include polymodal anion channels activated by both dopamine and tyramine, which may mediate inhibitory transmission by both molecules in vivo. Intriguingly, we also find that a novel serotonin-gated cation channel, LGC-50, is essential for aversive olfactory learning of pathogenic bacteria, a process known to depend on serotonergic neurotransmission. Remarkably, the redistribution of LGC-50 to neuronal processes is modulated by olfactory conditioning, and lgc-50 point mutations that cause misregulation of receptor membrane expression interfere with olfactory learning. Thus, the intracellular trafficking and localization of these receptors at synapses may represent a molecular cornerstone of the learning mechanism.

The glutamatergic synapse: a complex machinery for information processing

Being the most abundant synaptic type, the glutamatergic synapse is responsible for the larger part of the brain's information processing. Despite the conceptual simplicity of the basic mechanism of synaptic transmission, the glutamatergic synapse shows a large variation in the response to the presynaptic release of the neurotransmitter. This variability is observed not only among different synapses but also in the same single synapse. The synaptic response variability is due to several mechanisms of control of the information transferred among the neurons and suggests that the glutamatergic synapse is not a simple bridge for the transfer of information but plays an important role in its elaboration and management. The control of the synaptic information is operated at pre, post, and extrasynaptic sites in a sort of cooperation between the pre and postsynaptic neurons which also involves the activity of other neurons. The interaction between the different mechanisms of control is extremely complicated and its complete functionality is far from being fully understood. The present review, although not exhaustively, is intended to outline the most important of these mechanisms and their complexity, the understanding of which will be among the most intriguing challenges of future neuroscience.

AMPA receptor anchoring at CA1 synapses is determined by N-terminal domain and TARP γ8 interactions

AMPA receptor (AMPAR) abundance and positioning at excitatory synapses regulates the strength of transmission. Changes in AMPAR localisation can enact synaptic plasticity, allowing long-term information storage, and is therefore tightly controlled. Multiple mechanisms regulating AMPAR synaptic anchoring have been described, but with limited coherence or comparison between reports, our understanding of this process is unclear. Here, combining synaptic recordings from mouse hippocampal slices and super-resolution imaging in dissociated cultures, we compare the contributions of three AMPAR interaction domains controlling transmission at hippocampal CA1 synapses. We show that the AMPAR C-termini play only a modulatory role, whereas the extracellular N-terminal domain (NTD) and PDZ interactions of the auxiliary subunit TARP γ8 are both crucial, and each is sufficient to maintain transmission. Our data support a model in which γ8 accumulates AMPARs at the postsynaptic density, where the NTD further tunes their positioning. This interplay between cytosolic (TARP γ8) and synaptic cleft (NTD) interactions provides versatility to regulate synaptic transmission and plasticity.

Slow AMPA receptors in hippocampal principal cells

Glutamate receptor ion channels, including α-amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid (AMPA) receptors, mediate fast excitatory neurotransmission in the CNS. Previous work suggested that AMPA receptors produce a synaptic current with a millisecond duration. However, we find that about two-thirds of principal cells in the hippocampal CA1 region also express AMPA receptors with reduced desensitization that can stay active for half a second after repetitive stimuli. These slow AMPA receptors are expressed at about half of the synapses, with a flat spatial distribution. The increased charge transfer from slow AMPA receptors allows short-term potentiation from a postsynaptic locus and reliable triggering of action potentials. Biophysical and pharmacological observations imply slow AMPA receptors incorporate auxiliary proteins, and their activation lengthens miniature synaptic currents. These data indicate that AMPA receptors are a major source of synaptic diversity. Synapses harboring slow AMPA receptors could have unique roles in hippocampal function.

Subsynaptic positioning of AMPARs by LRRTM2 controls synaptic strength

Recent evidence suggests that nano-organization of proteins within synapses may control the strength of communication between neurons in the brain. The unique subsynaptic distribution of glutamate receptors, which cluster in nanoalignment with presynaptic sites of glutamate release, supports this hypothesis. However, testing it has been difficult because mechanisms controlling subsynaptic organization remain unknown. Reasoning that transcellular interactions could position AMPA receptors (AMPARs), we targeted a key transsynaptic adhesion molecule implicated in controlling AMPAR number, LRRTM2, using engineered, rapid proteolysis. Severing the LRRTM2 extracellular domain led quickly to nanoscale declustering of AMPARs away from release sites, not prompting their escape from synapses until much later. This rapid remodeling of AMPAR position produced significant deficits in evoked, but not spontaneous, postsynaptic receptor activation. These results dissociate receptor numbers from their nanopositioning in determination of synaptic function and support the novel concept that adhesion molecules acutely position receptors to dynamically control synaptic strength.

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.

Synaptic environment and extrasynaptic glutamate signals: The quest continues

Behaviour of a mammal relies on the brain's excitatory circuits equipped with glutamatergic synapses. In most cases, glutamate escaping from the synaptic cleft is rapidly buffered and taken up by high-affinity transporters expressed by nearby perisynaptic astroglial processes (PAPs). The spatial relationship between glutamatergic synapses and PAPs thus plays a crucial role in understanding glutamate signalling actions, yet its intricate features can only be fully appreciated using methods that operate beyond the diffraction limit of light. Here, we examine principal aspects pertaining to the receptor actions of glutamate, inside and outside the synaptic cleft in the brain, where the organisation of synaptic micro-physiology and micro-environment play a critical part. In what conditions and how far glutamate can escape the synaptic cleft activating its target receptors outside the immediate synapse has long been the subject of debate. Evidence is also emerging that neuronal activity- and astroglia-dependent glutamate spillover actions could be important across the spectrum of cognitive functions This article is part of the special issue on 'Glutamate Receptors - The Glutamatergic Synapse'.

miR-936 is Increased in Schizophrenia and Inhibits Neural Development and AMPA Receptor-Mediated Synaptic Transmission

MicroRNAs (miRNAs) are non-coding RNAs that regulate gene expression and play important roles in the development and function of synapses. miR-936 is a primate-specific miRNA increased in the dorsolateral prefrontal cortex (DLPFC) of individuals with schizophrenia. The significance of miR-936 increase to schizophrenia is unknown. Here, we show that miR-936 in the human DLPFC is enriched in cortical layer 2/3 and expressed in glutamatergic and GABAergic neurons. miR-936 is increased from layers 2 to 6 of the DLPFC in schizophrenia samples. In neurons derived from human induced pluripotent stem cells (iNs), miR-936 reduces the number of excitatory synapses, inhibits AMPA receptor-mediated synaptic transmission, and increases intrinsic excitability. These effects are mediated by its target gene TMOD2. These results indicate that miR-936 restricts the number of synapses and the strength of glutamatergic synaptic transmission by inhibiting TMOD2 expression. miR-936 upregulation in the DLPFC, therefore, can reduce glutamatergic synapses and weaken excitatory synaptic transmission, which underlie the synaptic pathology and hypofrontality in schizophrenia.

Structure and function of a neocortical synapse

In 1986, electron microscopy was used to reconstruct by hand the entire nervous system of a roundworm, the nematode Caenorhabditis elegans¹. Since this landmark study, high-throughput electron-microscopic techniques have enabled reconstructions of much larger mammalian brain circuits at synaptic resolution^2,3. Nevertheless, it remains unknown how the structure of a synapse relates to its physiological transmission strength-a key limitation for inferring brain function from neuronal wiring diagrams. Here we combine slice electrophysiology of synaptically connected pyramidal neurons in the mouse somatosensory cortex with correlated light microscopy and high-resolution electron microscopy of all putative synaptic contacts between the recorded neurons. We find a linear relationship between synapse size and strength, providing the missing link in assigning physiological weights to synapses reconstructed from electron microscopy. Quantal analysis also reveals that synapses contain at least 2.7 neurotransmitter-release sites on average. This challenges existing release models and provides further evidence that neocortical synapses operate with multivesicular release^4-6, suggesting that they are more complex computational devices than thought, and therefore expanding the computational power of the canonical cortical microcircuitry.

Asynchronous release sites align with NMDA receptors in mouse hippocampal synapses

Neurotransmitter is released synchronously and asynchronously following an action potential. Our recent study indicates that the release sites of these two phases are segregated within an active zone, with asynchronous release sites enriched near the center in mouse hippocampal synapses. Here we demonstrate that synchronous and asynchronous release sites are aligned with AMPA receptor and NMDA receptor clusters, respectively. Computational simulations indicate that this spatial and temporal arrangement of release can lead to maximal membrane depolarization through AMPA receptors, alleviating the pore-blocking magnesium leading to greater activation of NMDA receptors. Together, these results suggest that release sites are likely organized to activate NMDA receptors efficiently.

Imaging dendritic spines: molecular organization and signaling for plasticity

The structural plasticity of dendritic spines is considered to be essential for various forms of synaptic plasticity and, ultimately, learning and memory. The process is mediated by signaling pathways that promote the reorganization of the actin cytoskeleton and subsynaptic structures, which in turn cause structural and functional changes in dendritic spines. Recent advances in optical technologies have started to reveal the fine molecular structures and dynamic signaling occurring inside spines, providing significant insights into the molecular regulation of spines. Here, we highlight recent studies to resolve the molecular mechanisms underlying the spine actin cytoskeleton and plasticity with high spatiotemporal resolution. Moreover, we discuss new genome editing-based approaches in imaging the molecular structure and plasticity of dendritic spines.

Nanoscale co-organization and coactivation of AMPAR, NMDAR, and mGluR at excitatory synapses

The nanoscale co-organization of neurotransmitter receptors facing presynaptic release sites is a fundamental determinant of their coactivation and of synaptic physiology. At excitatory synapses, how endogenous AMPARs, NMDARs, and mGluRs are co-organized inside the synapse and their respective activation during glutamate release are still unclear. Combining single-molecule superresolution microscopy, electrophysiology, and modeling, we determined the average quantity of each glutamate receptor type, their nanoscale organization, and their respective activation. We observed that NMDARs form a unique cluster mainly at the center of the PSD, while AMPARs segregate in clusters surrounding the NMDARs. mGluR5 presents a different organization and is homogenously dispersed at the synaptic surface. From these results, we build a model predicting the synaptic transmission properties of a unitary synapse, allowing better understanding of synaptic physiology.

Cost Analysis of Treating Pediatric Supracondylar Humerus Fractures in Community Hospitals Compared With a Tertiary Care Hospital

OBJECTIVE

In the current healthcare environment, providing cost-efficient care is of paramount importance. One emerging strategy is to use community hospitals (CHs) rather than tertiary care hospitals (TCHs) for some procedures. This study assesses the costs of performing closed reduction percutaneous pinning (CRPP) of pediatric supracondylar humerus fractures (SCHFs) at a CH compared with a TCH.

METHODS

A retrospective review of 133 consecutive SCHFs treated with CRPP at a CH versus a TCH over a 6-year period was performed. Total encounter and subcategorized costs were compared between the procedures done at a CH versus those done at a TCH.

RESULTS

Performing CRPP for a SCHF at a CH compared with a TCH saved 44% in costs (P < 0.001). Cost reduction of 51% was attributable to operating room costs, 19% to anesthesia-related costs, 16% to imaging-related costs, and 7% to supplies.

DISCUSSION

Performing CRPP for a SCHF at a CH compared with a TCH results in a 44% decrease in direct cost, driven largely by surgical, anesthesia, and radiology-related savings.

Ultrastructural and functional changes at the tripartite synapse during epileptogenesis in a model of temporal lobe epilepsy

The persistent unresponsiveness of many of the acquired epilepsies to traditional antiseizure medications has motivated the search for prophylactic drug therapies that could reduce the incidence of epilepsy in this at risk population. These studies are based on the idea of a period of epileptogenesis that can follow a wide variety of brain injuries. Epileptogenesis is hypothesized to involve changes in the brain not initially associated with seizures, but which result finally in seizure prone networks. Understanding these changes will provide crucial clues for the development of prophylactic drugs. Using the repeated low-dose kainate rat model of epilepsy, we have studied the period of epileptogenesis following status epilepticus, verifying the latent period with continuous EEG monitoring. Focusing on ultrastructural properties of the tripartite synapse in the CA1 region of hippocampus we found increased astrocyte ensheathment around both the presynaptic and postsynaptic elements, reduced synaptic AMPA receptor subunit and perisynaptic astrocyte GLT-1 expression, and increased number of docked vesicles at the presynaptic terminal. These findings were associated with an increase in frequency of the mEPSCs observed in patch clamp recordings of CA1 pyramidal cells. The results suggest a complex set of changes, some of which have been associated with increasingly excitable networks such as increased vesicles and mEPSC frequency, and some associated with compensatory mechanisms, such as increased astrocyte ensheathment. The diversity of ultrastructural and electrophysiological changes observed during epileptogeneiss suggests that potential drug targets for this period should be broadened to include all components of the tripartite synapse.

Ultrastructural and molecular features of excitatory and glutamatergic synapses. The auditory nerve synapses

Glutamatergic synapses mediate fast synaptic transmission in the central nervous system. New developments highlight the importance of the synapse structural and molecular remodeling during development, aging and in neurological disorders. This chapter summarizes key structural and molecular aspects of the presynaptic and postsynaptic components of glutamatergic synapses in the brain. In addition, this chapter describes how the structure of the postsynaptic density and ionotropic glutamate content contribute to the function of auditory nerve synapses in the lower auditory brainstem.

Quantification of trans-synaptic protein alignment: A data analysis case for single-molecule localization microscopy

Nanoscale distribution of proteins and their relative positioning within a defined subcellular region are key to their physiological functions. Thanks to the super-resolution imaging methods, especially single-molecule localization microscopy (SMLM), mapping the three-dimensional distribution of multiple proteins has been easier and more efficient than ever. Nevertheless, in spite of the many tools available for efficient localization detection and image rendering, it has been a challenge to quantitatively analyze the 3D distribution and relative positioning of proteins in these SMLM data. Here, using heterogeneously distributed synaptic proteins as examples, we describe in detail a series of analytical methods including detection of nanoscale density clusters, quantification of the trans-synaptic alignment between these protein densities, and automatic en face projection and averaging. These analyses were performed within customized Matlab routines and we make the full scripts available. The concepts behind these analytical methods and the scripts can be adapted for quantitative analysis of spatial organization of other macromolecular complexes.

Unveiling the Extracellular Space of the Brain: From Super-resolved Microstructure to In Vivo Function

The extracellular space occupies approximately one-fifth of brain volume, molding a spider web of gaps filled with interstitial fluid and extracellular matrix where neurons and glial cells perform in concert. Yet, very little is known about the spatial organization and dynamics of the extracellular space, let alone its influence on brain function, owing to a lack of appropriate techniques (and a traditional bias toward the inside of cells, not the spaces in between). At the same time, it is clear that understanding fundamental brain functions, such as synaptic transmission, memory, sleep, and recovery from disease, calls for more focused research on the extracellular space of the brain. This review article highlights several key research areas, covering recent methodological and conceptual progress that illuminates this understudied, yet critically important, brain compartment, providing insights into the opportunities and challenges of this nascent field.

Specificity of Primate Amygdalar Pathways to Hippocampus

The amygdala projects to hippocampus in pathways through which affective or social stimuli may influence learning and memory. We investigated the still unknown amygdalar termination patterns and their postsynaptic targets in hippocampus from system to synapse in rhesus monkeys of both sexes. The amygdala robustly innervated the stratum lacunosum-moleculare layer of cornu ammonis fields and uncus anteriorly. Sparser terminations in posterior hippocampus innervated the radiatum and pyramidal layers at the prosubicular/CA1 juncture. The terminations, which were larger than other afferents in the surrounding neuropil, position the amygdala to influence hippocampal input anteriorly, and its output posteriorly. Most amygdalar boutons (76-80%) innervated spines of excitatory hippocampal neurons, and most of the remaining innervated presumed inhibitory neurons, identified by morphology and label with parvalbumin or calretinin, which distinguished nonoverlapping neurochemical classes of hippocampal inhibitory neurons. In CA1, amygdalar axons innervated some calretinin neurons, which disinhibit pyramidal neurons. By contrast, in CA3 the amygdala innervated both calretinin and parvalbumin neurons; the latter strongly inhibit nearby excitatory neurons. In CA3, amygdalar pathways also made closely spaced dual synapses on excitatory neurons. The strong excitatory synapses in CA3 may facilitate affective context representations and trigger sharp-wave ripples associated with memory consolidation. When the amygdala is excessively activated during traumatic events, the specialized innervation of excitatory neurons and the powerful parvalbumin inhibitory neurons in CA3 may allow the suppression of activity of nearby neurons that receive weaker nonamygdalar input, leading to biased passage of highly charged affective stimuli and generalized fear.SIGNIFICANCE STATEMENT Strong pathways from the amygdala targeted the anterior hippocampus, and more weakly its posterior sectors, positioned to influence a variety of emotional and cognitive functions. In hippocampal field CA1, the amygdala innervated some calretinin neurons, which disinhibit excitatory neurons. By contrast, in CA3 the amygdala innervated calretinin as well as some of the powerful parvalbumin inhibitory neurons and may help balance the activity of neural ensembles to allow social interactions, learning, and memory. These results suggest that when the amygdala is hyperactive during emotional upheaval, it strongly activates excitatory hippocampal neurons and parvalbumin inhibitory neurons in CA3, which can suppress nearby neurons that receive weaker input from other sources, biasing the passage of stimuli with high emotional import and leading to generalized fear.

Functional organization of postsynaptic glutamate receptors

Glutamate receptors are the most abundant excitatory neurotransmitter receptors in the brain, responsible for mediating the vast majority of excitatory transmission in neuronal networks. The AMPA- and NMDA-type ionotropic glutamate receptors (iGluRs) are ligand-gated ion channels that mediate the fast synaptic responses, while metabotropic glutamate receptors (mGluRs) are coupled to downstream signaling cascades that act on much slower timescales. These functionally distinct receptor sub-types are co-expressed at individual synapses, allowing for the precise temporal modulation of postsynaptic excitability and plasticity. Intriguingly, these receptors are differentially distributed with respect to the presynaptic release site. While iGluRs are enriched in the core of the synapse directly opposing the release site, mGluRs reside preferentially at the border of the synapse. As such, to understand the differential contribution of these receptors to synaptic transmission, it is important to not only consider their signaling properties, but also the mechanisms that control the spatial segregation of these receptor types within synapses. In this review, we will focus on the mechanisms that control the organization of glutamate receptors at the postsynaptic membrane with respect to the release site, and discuss how this organization could regulate synapse physiology.

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.

New approaches for solving old problems in neuronal protein trafficking

Fundamental cellular properties are determined by the repertoire and abundance of proteins displayed on the cell surface. As such, the trafficking mechanisms for establishing and maintaining the surface proteome must be tightly regulated for cells to respond appropriately to extracellular cues, yet plastic enough to adapt to ever-changing environments. Not only are the identity and abundance of surface proteins critical, but in many cases, their regulated spatial positioning within surface nanodomains can greatly impact their function. In the context of neuronal cell biology, surface levels and positioning of ion channels and neurotransmitter receptors play essential roles in establishing important properties, including cellular excitability and synaptic strength. Here we review our current understanding of the trafficking pathways that control the abundance and localization of proteins important for synaptic function and plasticity, as well as recent technological advances that are allowing the field to investigate protein trafficking with increasing spatiotemporal precision.

Gradation (approx. 10 size states) of synaptic strength by quantal addition of structural modules

Memory storage involves activity-dependent strengthening of synaptic transmission, a process termed long-term potentiation (LTP). The late phase of LTP is thought to encode long-term memory and involves structural processes that enlarge the synapse. Hence, understanding how synapse size is graded provides fundamental information about the information storage capability of synapses. Recent work using electron microscopy (EM) to quantify synapse dimensions has suggested that synapses may structurally encode as many as 26 functionally distinct states, which correspond to a series of proportionally spaced synapse sizes. Other recent evidence using super-resolution microscopy has revealed that synapses are composed of stereotyped nanoclusters of α-amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid (AMPA) receptors and scaffolding proteins; furthermore, synapse size varies linearly with the number of nanoclusters. Here we have sought to develop a model of synapse structure and growth that is consistent with both the EM and super-resolution data. We argue that synapses are composed of modules consisting of matrix material and potentially one nanocluster. LTP induction can add a trans-synaptic nanocluster to a module, thereby converting a silent module to an AMPA functional module. LTP can also add modules by a linear process, thereby producing an approximately 10-fold gradation in synapse size and strength.This article is part of the themed issue 'Integrating Hebbian and homeostatic plasticity'.