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

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.

Nano-organization of synaptic calcium signaling

Recent studies suggest an exquisite structural nano-organization within single synapses, where sites of evoked fusion - marked by clustering of synaptic vesicles, active zone proteins and voltage-gated calcium channels - are directly juxtaposed to postsynaptic receptor clusters within nanocolumns. This direct nanometer scale alignment between presynaptic fusion apparatus and postsynaptic receptors is thought to ensure the fidelity of synaptic signaling and possibly allow multiple distinct signals to occur without interference from each other within a single active zone. The functional specificity of this organization is made possible by the inherent nano-organization of calcium signals, where all the different calcium sources such as voltage-gated calcium channels, intracellular stores and store-operated calcium entry have dedicated local targets within their nanodomain to ensure precision of action. Here, we discuss synaptic nano-organization from the perspective of calcium signals, where some of the principal findings from early work in the 1980s continue to inspire current studies that exploit new genetic tools and super-resolution imaging technologies.

Synaptic architecture of a memory engram in the mouse hippocampus

Memory engrams are formed through experience-dependent remodeling of neural circuits, but their detailed architectures have remained unresolved. Using 3D electron microscopy, we performed nanoscale reconstructions of the hippocampal CA3-CA1 pathway following chemogenetic labeling of cellular ensembles with a remote history of correlated excitation during associative learning. Projection neurons involved in memory acquisition expanded their connectomes via multi-synaptic boutons without altering the numbers and spatial arrangements of individual axonal terminals and dendritic spines. This expansion was driven by presynaptic activity elicited by specific negative valence stimuli, regardless of the co-activation state of postsynaptic partners. The rewiring of initial ensembles representing an engram coincided with local, input-specific changes in the shapes and organelle composition of glutamatergic synapses, reflecting their weights and potential for further modifications. Our findings challenge the view that the connectivity among neuronal substrates of memory traces is governed by Hebbian mechanisms, and offer a structural basis for representational drifts.

Biophysical Modeling of Actin-Mediated Structural Plasticity Reveals Mechanical Adaptation in Dendritic Spines

Synaptic plasticity is important for learning and memory formation; it describes the strengthening or weakening of connections between synapses. The postsynaptic part of excitatory synapses resides in dendritic spines, which are small protrusions on the dendrites. One of the key features of synaptic plasticity is its correlation with the size of these spines. A long-lasting synaptic strength increase [long-term potentiation (LTP)] is only possible through the reconfiguration of the actin spine cytoskeleton. Here, we develop an experimentally informed three-dimensional computational model in a moving boundary framework to investigate this reconfiguration. Our model describes the reactions between actin and actin-binding proteins leading to the cytoskeleton remodeling and their effect on the spine membrane shape to examine the spine enlargement upon LTP. Moreover, we find that the incorporation of perisynaptic elements enhances spine enlargement upon LTP, exhibiting the importance of accounting for these elements when studying structural LTP. Our model shows adaptation to repeated stimuli resulting from the interactions between spine proteins and mechanical forces.

Conditioned morphine tolerance promotes neurogenesis, dendritic remodelling and pro-plasticity molecules in the adult rat hippocampus

Structural neuroplasticity of the hippocampus in the form of neurogenesis and dendritic remodelling underlying morphine tolerance is still less known. Therefore, in this study, we aimed to assess whether unconditioned- and conditioned-morphine tolerance can trigger structural neuroplasticity in the dorsal and ventral parts of the adult male rat hippocampus. Evaluation of the levels of neurogenesis markers (Ki67 and DCX) by immunohistochemistry shows that conditioned morphine tolerance is sufficient to increase the baseline topographic level of hippocampal neurogenesis in adult rats. Dendritic spine visualization by Golgi staining shows that the behavioural testing paradigms themselves are sufficient to trigger the hippocampus subregion-specific changes in the dendritic remodelling along the apical dendrites of hippocampal CA1 pyramidal neurons and dentate granule cells in adult rats. Quantitative reverse transcription polymerase chain reaction of Bdnf, Trkb, Rac-1 and RhoA mRNA levels as pro-plasticity molecules, shows that the conditioned morphine tolerance is effective in changing Bdnf and RhoA mRNA levels in the ventral hippocampus of adult rats. In summary, we demonstrate that the acquisition of morphine tolerance promotes adult neurogenesis, dendritic remodelling and pro-plasticity molecules such as Bdnf/Trkb in the rat hippocampus. Indeed, the structural neuroplasticity of the hippocampus may underlie the newly formed aberrant memory and could provide the initial basis for understanding the neurobiological mechanisms of morphine-tolerance plasticity in the hippocampus.

Structural and biochemical alterations in dendritic spines as key mechanisms for severe mental illnesses

Severe mental illnesses (SMI) collectively affect approximately 20% of the global population, as estimated by the World Health Organization (WHO). Despite having diverse etiologies, clinical symptoms, and pharmacotherapies, these diseases share a common pathophysiological characteristic: the misconnection of brain areas involved in reality perception, executive control, and cognition, including the corticolimbic system. Dendritic spines play a crucial role in excitatory neurotransmission within the central nervous system. These small structures exhibit remarkable plasticity, regulated by factors such as neurotransmitter tone, neurotrophic factors, and innate immunity-related molecules, and other mechanisms - all of which are associated with the pathophysiology of SMI. However, studying dendritic spine mechanisms in both healthy and pathological conditions in patients is fraught with technical limitations. This is where animal models related to these diseases become indispensable. They have played a pivotal role in elucidating the significance of dendritic spines in SMI. In this review, the information regarding the potential role of dendritic spines in SMI was summarized, drawing from clinical and animal model reports. Also, the implications of targeting dendritic spine-related molecules for SMI treatment were explored. Specifically, our focus is on major depressive disorder and the neurodevelopmental disorders schizophrenia and autism spectrum disorder. Abundant clinical and basic research has studied the functional and structural plasticity of dendritic spines in these diseases, along with potential pharmacological targets that modulate the dynamics of these structures. These targets may be associated with the clinical efficacy of the pharmacotherapy.

Ion-concentration gradients induced by synaptic input increase the voltage depolarization in dendritic spines

The vast majority of excitatory synaptic connections occur on dendritic spines. Due to their extremely small volume and spatial segregation from the dendrite, even moderate synaptic currents can significantly alter ionic concentrations. This results in chemical potential gradients between the dendrite and the spine head, leading to measurable electrical currents. In modeling electric signals in spines, different formalisms were previously used. While the cable equation is fundamental for understanding the electrical potential along dendrites, it only considers electrical currents as a result of gradients in electrical potential. The Poisson-Nernst-Planck (PNP) equations offer a more accurate description for spines by incorporating both electrical and chemical potential. However, solving PNP equations is computationally complex. In this work, diffusion currents are incorporated into the cable equation, leveraging an analogy between chemical and electrical potential. For simulating electric signals based on this extension of the cable equation, a straightforward numerical solver is introduced. The study demonstrates that this set of equations can be accurately solved using an explicit finite difference scheme. Through numerical simulations, this study unveils a previously unrecognized mechanism involving diffusion currents that amplify electric signals in spines. This discovery holds crucial implications for both numerical simulations and experimental studies focused on spine neck resistance and calcium signaling in dendritic spines.

Making time and space for calcium control of neuron activity

Calcium directly controls or indirectly regulates numerous functions that are critical for neuronal network activity. Intracellular calcium concentration is tightly regulated by numerous molecular mechanisms because spatial domains and temporal dynamics (not just peak amplitude) are critical for calcium control of synaptic plasticity and ion channel activation, which in turn determine neuron spiking activity. The computational models investigating calcium control are valuable because experiments achieving high spatial and temporal resolution simultaneously are technically unfeasible. Simulations of calcium nanodomains reveal that specific calcium sources can couple to specific calcium targets, providing a mechanism to determine the direction of synaptic plasticity. Cooperativity of calcium domains opposes specificity, suggesting that the dendritic branch might be the preferred computational unit of the neuron.

Spine apparatus modulates Ca 2+ in spines through spatial localization of sources and sinks

Dendritic spines are small protrusions on dendrites in neurons and serve as sites of postsynaptic activity. Some of these spines contain smooth endoplasmic reticulum (SER), and sometimes an even further specialized SER known as the spine apparatus (SA). In this work, we developed a stochastic spatial model to investigate the role of the SER and the SA in modulating Ca 2+ dynamics. Using this model, we investigated how ryanodine receptor (RyR) localization, spine membrane geometry, and SER geometry can impact Ca 2+ transients in the spine and in the dendrite. Our simulations found that RyR opening is dependent on where it is localized in the SER and on the SER geometry. In order to maximize Ca 2+ in the dendrites (for activating clusters of spines and spine-spine communication), a laminar SA was favorable with RyRs localized in the neck region, closer to the dendrite. We also found that the presence of the SER without the laminar structure, coupled with RyR localization at the head, leads to higher Ca 2+ presence in the spine. These predictions serve as design principles for understanding how spines with an ER can regulate Ca 2+ dynamics differently from spines without ER through a combination of geometry and receptor localization.

Highlights

1RyR opening in dendritic spine ER is location dependent and spine geometry dependent. Ca 2+ buffers and SERCA can buffer against runaway potentiation of spines even when CICR is activated. RyRs located towards the ER neck allow for more Ca 2+ to reach the dendrites. RyRs located towards the spine head are favorable for increased Ca 2+ in spines.

Impact of a pyridazine derivative on tripartite synapse ultrastructure in hippocampus: a three-dimensional analysis

Introduction

We previously discovered a pyridazine derivative compound series that can improve cognitive functions in mouse models of Alzheimer's disease. One of the advanced compounds from this series, LDN/OSU-0215111-M3, was selected as the preclinical development candidate. This compound activates local protein translation at the perisynaptic astrocytic process (PAP) and enhances synaptic plasticity sequentially. While biochemical evidence supports the hypothesis that the compound enhances the structural plasticity of the tripartite synapse, its direct structural impact has not been investigated.

Methods

Volume electron microscopy was used to study the hippocampal tripartite synapse three-dimensional structure in 3-month-old wild-type FVB/NJ mice after LDN/OSU-0215111-M3 treatment.

Results

LDN/OSU-0215111-M3 increased the size of tertiary apical dendrites, the volume of mushroom spines, the proportion of mushroom spines containing spine apparatus, and alterations in the spine distribution across the surface area of tertiary dendrites. Compound also increased the number of the PAP interacting with the mushroom spines as well as the size of the PAP in contact with the spines. Furthermore, proteomic analysis of the isolated synaptic terminals indicated an increase in dendritic and synaptic proteins as well as suggested a possible involvement of the phospholipase D signaling pathway. To further validate that LDN/OSU-0215111-M3 altered synaptic function, electrophysiological studies showed increased long-term potentiation following compound treatment.

Discussion

This study provides direct evidence that pyridazine derivatives enhance the structural and functional plasticity of the tripartite synapse.

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.

Computational modeling of AMPK and mTOR crosstalk in glutamatergic synapse calcium signaling

Neuronal energy consumption is vital for information processing and memory formation in synapses. The brain consists of just 2% of the human body's mass, but consumes almost 20% of the body's energy budget. Most of this energy is attributed to active transport in ion signaling, with calcium being the canonical second messenger of synaptic transmission. Here, we develop a computational model of synaptic signaling resulting in the activation of two protein kinases critical in metabolic regulation and cell fate, AMP-Activated protein kinase (AMPK) and mammalian target of rapamycin (mTOR) and investigate the effect of glutamate stimulus frequency on their dynamics. Our model predicts that frequencies of glutamate stimulus over 10 Hz perturb AMPK and mTOR oscillations at higher magnitudes by up to 36% and change the area under curve (AUC) by 5%. This dynamic difference in AMPK and mTOR activation trajectories potentially differentiates high frequency stimulus bursts from basal neuronal signaling leading to a downstream change in synaptic plasticity. Further, we also investigate the crosstalk between insulin receptor and calcium signaling on AMPK and mTOR activation and predict that the pathways demonstrate multistability dependent on strength of insulin signaling and metabolic consumption rate. Our predictions have implications for improving our understanding of neuronal metabolism, synaptic pruning, and synaptic plasticity.

Neural activity induces strongly coupled electro-chemo-mechanical interactions and fluid flow in astrocyte networks and extracellular space-A computational study

The complex interplay between chemical, electrical, and mechanical factors is fundamental to the function and homeostasis of the brain, but the effect of electrochemical gradients on brain interstitial fluid flow, solute transport, and clearance remains poorly quantified. Here, via in-silico experiments based on biophysical modeling, we estimate water movement across astrocyte cell membranes, within astrocyte networks, and within the extracellular space (ECS) induced by neuronal activity, and quantify the relative role of different forces (osmotic, hydrostatic, and electrical) on transport and fluid flow under such conditions. We find that neuronal activity alone may induce intracellular fluid velocities in astrocyte networks of up to 14μm/min, and fluid velocities in the ECS of similar magnitude. These velocities are dominated by an osmotic contribution in the intracellular compartment; without it, the estimated fluid velocities drop by a factor of ×34-45. Further, the compartmental fluid flow has a pronounced effect on transport: advection accelerates ionic transport within astrocytic networks by a factor of ×1-5 compared to diffusion alone.

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.

A multifarious exploration of synaptic tagging and capture hypothesis in synaptic plasticity: Development of an integrated mathematical model and computational experiments

The synaptic tagging and capture (STC) hypothesis not only explain the integration and association of synaptic activities, but also the formation of learning and memory. The synaptic pathways involved in the synaptic tagging and capture phenomenon are called STC pathways. The STC hypothesis provides a potential explanation of the neuronal and synaptic processes underlying the synaptic consolidation of memories. Several mechanisms and molecules have been proposed to explain the process of memory allocation and synaptic tags, respectively. However, a clear link between the STC hypothesis and memory allocation is still missing because the encoding of memories in neural circuits is mainly associated with strongly recurrently connected groups of neurons. To explore the mechanisms of potential synaptic tagging candidates and their involvement in the process of memory allocation, we develop a mathematical model for a single dendritic spine based on five essential criteria of a synaptic tag. By developing a mathematical model, we attempt to understand the roles of the potentially critical molecular networks underlying the STC and the essential attributes of a synaptic tag. We include essential memory molecules in the STC model that have been identified in earlier studies as crucial for STC pathways. CaMKII activation is critical for the setting of the initial tag; however, coordinated activities with other kinases and the biochemical pathways are necessary for the tag to be stable. PKA modulates NMDAR-mediated Ca²⁺ signalling. Similarly, PKA and ERK crosstalk is essential for Ca²⁺ - mediated protein synthesis during l-LTP. Our theoretical model explains the quantitative contribution of Tags and protein synthesis during l-LTP in synaptic strength.

Cells of the Central Nervous System: An Overview of Their Structure and Function

The central nervous system is the last major organ system in the vertebrate body to yield its cellular structure, due to the complexity of its cells and their interactions. The fundamental unit of the nervous system is the neuron, which forms complex circuits that receive and integrate information and generate adaptive responses. Each neuron is composed of an input domain consisting of multiple dendrites along with the cell body, which is also responsible for the majority of macromolecule synthesis for the cell. The output domain is the axon which is a singular extension from the cell body that propagates the action potential to the synapse, where signals pass from one neuron to another. Facilitating these functions are cohorts of supporting cells consisting of astrocytes, oligodendrocytes and microglia along with NG2 cells and ependymal cells. Astrocytes have a dazzling array of functions including physical support, maintenance of homeostasis, development and integration of synaptic activity. Oligodendrocytes form the myelin sheath which surrounds axons and enables rapid conduction of the nerve impulse. Microglia are the resident immune cells, providing immune surveillance and remodeling of neuronal circuits during development and trauma. All these cells function in concert with each other, producing the remarkably diverse functions of the nervous system.

Methodology for development of single cell dendritic spine (SCDS) synaptic tagging and capture model using Virtual Cell (VCell)

Single cell dendritic spine modelling methodology has been adopted to explain structural plasticity and respective change in the neuronal volume previously. However, the single cell dendrite methodology has not been employed previously to explain one of the important aspects of memory allocation i.e., Synaptic tagging and Capture (STC) hypothesis. It is difficult to relate the physical properties of STC pathways to structural changes and synaptic strength. We create a mathematical model based on earlier reported synaptic tagging networks. We built the model using Virtual Cell (VCell) software and used it to interpret experimental data and investigate the behavior and characteristics of known Synaptic tagging candidates.•We investigate processes associated with synaptic tagging candidates and compare them to the assumptions based on the STC hypothesis.•We assess the behavior of several reported synaptic tagging candidates against the requirements outlined in the synaptic tagging hypothesis.

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.

Dendritic spine morphology regulates calcium-dependent synaptic weight change

Dendritic spines act as biochemical computational units and must adapt their responses according to their activation history. Calcium influx acts as the first signaling step during postsynaptic activation and is a determinant of synaptic weight change. Dendritic spines also come in a variety of sizes and shapes. To probe the relationship between calcium dynamics and spine morphology, we used a stochastic reaction-diffusion model of calcium dynamics in idealized and realistic geometries. We show that despite the stochastic nature of the various calcium channels, receptors, and pumps, spine size and shape can modulate calcium dynamics and subsequently synaptic weight updates in a deterministic manner. Through a series of exhaustive simulations and analyses, we found that the calcium dynamics and synaptic weight change depend on the volume-to-surface area of the spine. The relationships between calcium dynamics and spine morphology identified in idealized geometries also hold in realistic geometries, suggesting that there are geometrically determined deterministic relationships that may modulate synaptic weight change.

Functional and multiscale 3D structural investigation of brain tissue through correlative in vivo physiology, synchrotron microtomography and volume electron microscopy

Understanding the function of biological tissues requires a coordinated study of physiology and structure, exploring volumes that contain complete functional units at a detail that resolves the relevant features. Here, we introduce an approach to address this challenge: Mouse brain tissue sections containing a region where function was recorded using in vivo 2-photon calcium imaging were stained, dehydrated, resin-embedded and imaged with synchrotron X-ray computed tomography with propagation-based phase contrast (SXRT). SXRT provided context at subcellular detail, and could be followed by targeted acquisition of multiple volumes using serial block-face electron microscopy (SBEM). In the olfactory bulb, combining SXRT and SBEM enabled disambiguation of in vivo-assigned regions of interest. In the hippocampus, we found that superficial pyramidal neurons in CA1a displayed a larger density of spine apparati than deeper ones. Altogether, this approach can enable a functional and structural investigation of subcellular features in the context of cells and tissues.

Reinforcing Interdisciplinary Collaborations to Unravel the Astrocyte "Calcium Code"

In this review article, we present the major insights from and challenges faced in the acquisition, analysis and modeling of astrocyte calcium activity, aiming at bridging the gap between those fields to crack the complex astrocyte “Calcium Code”. We then propose strategies to reinforce interdisciplinary collaborative projects to unravel astrocyte function in health and disease.

Can biophysical models of dendritic spines be used to explore synaptic changes associated with addiction?

Effective treatments that prevent or reduce drug relapse vulnerability should be developed to relieve the high burden of drug addiction on society. This will only be possible by enhancing the understanding of the molecular mechanisms underlying the neurobiology of addiction. Recent experimental data have shown that dendritic spines, small protrusions from the dendrites that receive excitatory input, of spiny neurons in the nucleus accumbens exhibit morphological changes during drug exposure and withdrawal. Moreover, these changes relate to the characteristic drug-seeking behavior of addiction. However, due to the complexity of the dendritic spines, we do not yet fully understand the processes underlying their structural changes in response to different inputs. We propose that biophysical models can enhance the current understanding of these processes by incorporating different, and sometimes, discrepant experimental data to identify the shared underlying mechanisms and generate experimentally testable hypotheses. This review aims to give an up-to-date report on biophysical models of dendritic spines, focusing on those models that describe their shape changes, which are well-known to relate to learning and memory. Moreover, it examines how these models can enhance our understanding of the effect of the drugs and the synaptic changes during withdrawal, as well as during neurodegenerative disease progression such as Alzheimer's disease.

Role of the endoplasmic reticulum in synaptic transmission

Neurons possess a complex morphology spanning long distances and a large number of subcellular specializations such as presynaptic terminals and dendritic spines. This structural complexity is essential for maintenance of synaptic junctions and associated electrical as well as biochemical signaling events. Given the structural and functional complexity of neurons, neuronal endoplasmic reticulum is emerging as a key regulator of neuronal function, in particular synaptic signaling. Neuronal endoplasmic reticulum mediates calcium signaling, calcium and lipid homeostasis, vesicular trafficking, and proteostasis events that underlie autonomous functions of numerous subcellular compartments. However, based on its geometric complexity spanning the whole neuron, endoplasmic reticulum also integrates the activity of these autonomous compartments across the neuron and coordinates their interactions with the soma. In this article, we review recent work regarding neuronal endoplasmic reticulum function and its relationship to neurotransmission and plasticity.

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.

Morphological principles of neuronal mitochondria

In the highly dynamic metabolic landscape of a neuron, mitochondrial membrane architectures can provide critical insight into the unique energy balance of the cell. Current theoretical calculations of functional outputs like adenosine triphosphate and heat often represent mitochondria as idealized geometries, and therefore, can miscalculate the metabolic fluxes. To analyze mitochondrial morphology in neurons of mouse cerebellum neuropil, 3D tracings of complete synaptic and axonal mitochondria were constructed using a database of serial transmission electron microscopy (TEM) tomography images and converted to watertight meshes with minimal distortion of the original microscopy volumes with a granularity of 1.64 nanometer isotropic voxels. The resulting in-silico representations were subsequently quantified by differential geometry methods in terms of the mean and Gaussian curvatures, surface areas, volumes, and membrane motifs, all of which can alter the metabolic output of the organelle. Finally, we identify structural motifs present across this population of mitochondria, which may contribute to future modeling studies of mitochondrial physiology and metabolism in neurons.

Nanoscale molecular architecture controls calcium diffusion and ER replenishment in dendritic spines

Dendritic spines are critical components of neuronal synapses as they receive and transform synaptic inputs into a succession of calcium-regulated biochemical events. The spine apparatus (SA), an extension of smooth endoplasmic reticulum, regulates slow and fast calcium dynamics in spines. Calcium release events deplete SA calcium ion reservoir rapidly, yet the next cycle of signaling requires its replenishment. How spines achieve this replenishment without triggering calcium release remains unclear. Using computational modeling, calcium and STED superresolution imaging, we show that the SA replenishment involves the store-operated calcium entry pathway during spontaneous calcium transients. We identified two main conditions for SA replenishment without depletion: a small amplitude and a slow timescale for calcium influx, and a close proximity between SA and plasma membranes. Thereby, spine’s nanoscale organization separates SA replenishment from depletion. We further conclude that spine’s receptor organization also determines the calcium dynamics during the induction of long-term synaptic changes.

Occurrence of Calcium Oscillations in Human Spermatozoa Is Based on Spatial Signaling Enzymes Distribution

In human spermatozoa, calcium dynamics control most of fertilization events. Progesterone, present in the female reproductive system, can trigger several types of calcium responses, such as low-frequency oscillations. Here we aimed to identify the mechanisms of progesterone-induced calcium signaling in human spermatozoa. Progesterone-induced activation of fluorophore-loaded spermatozoa was studied by fluorescent microscopy. Two computational models were developed to describe the spermatozoa calcium responses: a homogeneous one based on a system of ordinary differential equations and a three-dimensional one with added space dimensions and diffusion for the cytosolic species. In response to progesterone, three types of calcium responses were observed in human spermatozoa: a single transient rise of calcium concentration in cytosol, a steady elevation, or low-frequency oscillations. The homogenous model provided qualitative description of the oscillatory and the single spike responses, while the three-dimensional model captured the calcium peak shape and the frequency of calcium oscillations. The model analysis demonstrated that an increase in the calcium diffusion coefficient resulted in the disappearance of the calcium oscillations. Additionally, in silico analysis suggested that the spatial distribution of calcium signaling enzymes governs the appearance of calcium oscillations in progesterone-activated human spermatozoa.

Mechanical Principles Governing the Shapes of Dendritic Spines

Dendritic spines are small, bulbous protrusions along the dendrites of neurons and are sites of excitatory postsynaptic activity. The morphology of spines has been implicated in their function in synaptic plasticity and their shapes have been well-characterized, but the potential mechanics underlying their shape development and maintenance have not yet been fully understood. In this work, we explore the mechanical principles that could underlie specific shapes using a minimal biophysical model of membrane-actin interactions. Using this model, we first identify the possible force regimes that give rise to the classic spine shapes-stubby, filopodia, thin, and mushroom-shaped spines. We also use this model to investigate how the spine neck might be stabilized using periodic rings of actin or associated proteins. Finally, we use this model to predict that the cooperation between force generation and ring structures can regulate the energy landscape of spine shapes across a wide range of tensions. Thus, our study provides insights into how mechanical aspects of actin-mediated force generation and tension can play critical roles in spine shape maintenance.

Systems modeling predicts that mitochondria ER contact sites regulate the postsynaptic energy landscape

Spatiotemporal compartmentation of calcium dynamics is critical for neuronal function, particularly in postsynaptic spines. This exquisite level of Ca²⁺ compartmentalization is achieved through the storage and release of Ca²⁺ from various intracellular organelles particularly the endoplasmic reticulum (ER) and the mitochondria. Mitochondria and ER are established storage organelles controlling Ca²⁺ dynamics in neurons. Mitochondria also generate a majority of energy used within postsynaptic spines to support the downstream events associated with neuronal stimulus. Recently, high resolution microscopy has unveiled direct contact sites between the ER and the mitochondria (MERCs), which directly channel Ca²⁺ release from the ER into the mitochondrial membrane. In this study, we develop a computational 3D reaction-diffusion model to investigate the role of MERCs in regulating Ca²⁺ and ATP dynamics. This spatiotemporal model accounts for Ca²⁺ oscillations initiated by glutamate stimulus of metabotropic and ionotropic glutamate receptors and Ca²⁺ changes in four different compartments: cytosol, ER, mitochondria, and the MERC microdomain. Our simulations predict that the organization of these organelles and inter-organellar contact sites play a key role in modulating Ca²⁺ and ATP dynamics.

We further show that the crosstalk between geometry (mitochondria and MERC) and metabolic parameters (cytosolic ATP hydrolysis, ATP generation) influences the neuronal energy state. Our findings shed light on the importance of organelle interactions in predicting Ca²⁺ dynamics in synaptic signaling. Overall, our model predicts that a combination of MERC linkage and mitochondria size is necessary for optimal ATP production in the cytosol.

Ultrastructural analysis of dendritic spine necks reveals a continuum of spine morphologies

Dendritic spines are membranous protrusions that receive essentially all excitatory inputs in most mammalian neurons. Spines, with a bulbous head connected to the dendrite by a thin neck, have a variety of morphologies that likely impact their functional properties. Nevertheless, the question of whether spines belong to distinct morphological subtypes is still open. Addressing this quantitatively requires clear identification and measurements of spine necks. Recent advances in electron microscopy enable large-scale systematic reconstructions of spines with nanometer precision in 3D. Analyzing ultrastructural reconstructions from mouse neocortical neurons with computer vision algorithms, we demonstrate that the vast majority of spine structures can be rigorously separated into heads and necks, enabling morphological measurements of spine necks. We then used a database of spine morphological parameters to explore the potential existence of different spine classes. Without exception, our analysis revealed unimodal distributions of individual morphological parameters of spine heads and necks, without evidence for subtypes of spines. The postsynaptic density size was strongly correlated with the spine head volume. The spine neck diameter, but not the neck length, was also correlated with the head volume. Spines with larger head volumes often had a spine apparatus and pairs of spines in a post-synaptic cell contacted by the same axon had similar head volumes. Our data reveal a lack of morphological subtypes of spines and indicate that the spine neck length and head volume must be independently regulated. These results have repercussions for our understanding of the function of dendritic spines in neuronal circuits.

Stochastic reaction-diffusion modeling of calcium dynamics in 3D dendritic spines of Purkinje cells

Calcium (Ca²⁺) is a second messenger assumed to control changes in synaptic strength in the form of both long-term depression and long-term potentiation at Purkinje cell dendritic spine synapses via inositol trisphosphate (IP₃)-induced Ca²⁺ release. These Ca²⁺ transients happen in response to stimuli from parallel fibers (PFs) from granule cells and climbing fibers (CFs) from the inferior olivary nucleus. These events occur at low numbers of free Ca²⁺, requiring stochastic single-particle methods when modeling them. We use the stochastic particle simulation program MCell to simulate Ca²⁺ transients within a three-dimensional Purkinje cell dendritic spine. The model spine includes the endoplasmic reticulum, several Ca²⁺ transporters, and endogenous buffer molecules. Our simulations successfully reproduce properties of Ca²⁺ transients in different dynamical situations. We test two different models of the IP₃ receptor (IP₃R). The model with nonlinear concentration response of binding of activating Ca²⁺ reproduces experimental results better than the model with linear response because of the filtering of noise. Our results also suggest that Ca²⁺-dependent inhibition of the IP₃R needs to be slow to reproduce experimental results. Simulations suggest the experimentally observed optimal timing window of CF stimuli arises from the relative timing of CF influx of Ca²⁺ and IP₃ production sensitizing IP₃R for Ca²⁺-induced Ca²⁺ release. We also model ataxia, a loss of fine motor control assumed to be the result of malfunctioning information transmission at the granule to Purkinje cell synapse, resulting in a decrease or loss of Ca²⁺ transients. Finally, we propose possible ways of recovering Ca²⁺ transients under ataxia.

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.

Nanoscale 3D EM reconstructions reveal intrinsic mechanisms of structural diversity of chemical synapses

Chemical synapses of shared cellular origins have remarkably heterogeneous structures, but how this diversity is generated is unclear. Here, we use three-dimensional (3D) electron microscopy and artificial intelligence algorithms for image processing to reconstruct functional excitatory microcircuits in the mouse hippocampus and microcircuits in which neurotransmitter signaling is permanently suppressed with genetic tools throughout the lifespan. These nanoscale analyses reveal that experience is dispensable for morphogenesis of synapses with different geometric shapes and contents of membrane organelles and that arrangement of morphologically distinct connections in local networks is stochastic. Moreover, loss of activity increases the variability in sizes of opposed pre- and postsynaptic structures without disrupting their alignments, suggesting that inherently variable weights of naive connections become progressively matched with repetitive use. These results demonstrate that mechanisms for the structural diversity of neuronal synapses are intrinsic and provide insights into how circuits essential for memory storage assemble and integrate information.

Depression patient-derived cortical neurons reveal potential biomarkers for antidepressant response

Major depressive disorder is highly prevalent worldwide and has been affecting an increasing number of people each year. Current first line antidepressants show merely 37% remission, and physicians are forced to use a trial-and-error approach when choosing a single antidepressant out of dozens of available medications. We sought to identify a method of testing that would provide patient-specific information on whether a patient will respond to a medication using in vitro modeling. Patient-derived lymphoblastoid cell lines from the Sequenced Treatment Alternatives to Relieve Depression study were used to rapidly generate cortical neurons and screen them for bupropion effects, for which the donor patients showed remission or non-remission. We provide evidence for biomarkers specific for bupropion response, including synaptic connectivity and morphology changes as well as specific gene expression alterations. These biomarkers support the concept of personalized antidepressant treatment based on in vitro platforms and could be utilized as predictors to patient response in the clinic.

Abnormalities of synaptic mitochondria in autism spectrum disorder and related neurodevelopmental disorders

Autism spectrum disorder (ASD) is a neurodevelopmental condition primarily characterized by an impairment of social interaction combined with the occurrence of repetitive behaviors. ASD starts in childhood and prevails across the lifespan. The variability of its clinical presentation renders early diagnosis difficult. Mutations in synaptic genes and alterations of mitochondrial functions are considered important underlying pathogenic factors, but it is obvious that we are far from a comprehensive understanding of ASD pathophysiology. At the synapse, mitochondria perform diverse functions, which are clearly not limited to their classical role as energy providers. Here, we review the current knowledge about mitochondria at the synapse and summarize the mitochondrial disturbances found in mouse models of ASD and other ASD-related neurodevelopmental disorders, like DiGeorge syndrome, Rett syndrome, Tuberous sclerosis complex, and Down syndrome.

Cell shape regulates subcellular organelle location to control early Ca2+ signal dynamics in vascular smooth muscle cells

The shape of the cell is connected to its function; however, we do not fully understand underlying mechanisms by which global shape regulates a cell's functional capabilities. Using theory, experiments and simulation, we investigated how physiologically relevant cell shape changes affect subcellular organization, and consequently intracellular signaling, to control information flow needed for phenotypic function. Vascular smooth muscle cells going from a proliferative and motile circular shape to a contractile fusiform shape show changes in the location of the sarcoplasmic reticulum, inter-organelle distances, and differential distribution of receptors in the plasma membrane. These factors together lead to the modulation of signals transduced by the M3 muscarinic receptor/Gq/PLCβ pathway at the plasma membrane, amplifying Ca2+ dynamics in the cytoplasm, and the nucleus resulting in phenotypic changes, as determined by increased activity of myosin light chain kinase in the cytoplasm and enhanced nuclear localization of the transcription factor NFAT. Taken together, our observations show a systems level phenomenon whereby global cell shape affects subcellular organization to modulate signaling that enables phenotypic changes.

Structural LTP: from synaptogenesis to regulated synapse enlargement and clustering

Nature teaches us that form precedes function, yet structure and function are intertwined. Such is the case with synapse structure, function, and plasticity underlying learning, especially in the hippocampus, a crucial brain region for memory formation. As the hippocampus matures, enduring changes in synapse structure produced by long-term potentiation (LTP) shift from synaptogenesis to synapse enlargement that is homeostatically balanced by stalled spine outgrowth and local spine clustering. Production of LTP leads to silent spine outgrowth at P15, and silent synapse enlargement in adult hippocampus at 2hours, but not at 5 or 30min following induction. Here we consider structural LTP in the context of developmental stage and variation in the availability of local resources of endosomes, smooth endoplasmic reticulum and polyribosomes. The emerging evidence supports a need for more nuanced analysis of synaptic plasticity in the context of subcellular resource availability and developmental stage.

3D mesh processing using GAMer 2 to enable reaction-diffusion simulations in realistic cellular geometries

Recent advances in electron microscopy have enabled the imaging of single cells in 3D at nanometer length scale resolutions. An uncharted frontier for in silico biology is the ability to simulate cellular processes using these observed geometries. Enabling such simulations requires watertight meshing of electron micrograph images into 3D volume meshes, which can then form the basis of computer simulations of such processes using numerical techniques such as the finite element method. In this paper, we describe the use of our recently rewritten mesh processing software, GAMer 2, to bridge the gap between poorly conditioned meshes generated from segmented micrographs and boundary marked tetrahedral meshes which are compatible with simulation. We demonstrate the application of a workflow using GAMer 2 to a series of electron micrographs of neuronal dendrite morphology explored at three different length scales and show that the resulting meshes are suitable for finite element simulations. This work is an important step towards making physical simulations of biological processes in realistic geometries routine. Innovations in algorithms to reconstruct and simulate cellular length scale phenomena based on emerging structural data will enable realistic physical models and advance discovery at the interface of geometry and cellular processes. We posit that a new frontier at the intersection of computational technologies and single cell biology is now open.

An Open-Source Mesh Generation Platform for Biophysical Modeling Using Realistic Cellular Geometries

Advances in imaging methods such as electron microscopy, tomography, and other modalities are enabling high-resolution reconstructions of cellular and organelle geometries. Such advances pave the way for using these geometries for biophysical and mathematical modeling once these data can be represented as a geometric mesh, which, when carefully conditioned, enables the discretization and solution of partial differential equations. In this work, we outline the steps for a naïve user to approach the Geometry-preserving Adaptive MeshER software version 2, a mesh generation code written in C++ designed to convert structural data sets to realistic geometric meshes while preserving the underlying shapes. We present two example cases: 1) mesh generation at the subcellular scale as informed by electron tomography and 2) meshing a protein with a structure from x-ray crystallography. We further demonstrate that the meshes generated by the Geometry-preserving Adaptive MeshER software are suitable for use with numerical methods. Together, this collection of libraries and tools simplifies the process of constructing realistic geometric meshes from structural biology data.

Roles for the Endoplasmic Reticulum in Regulation of Neuronal Calcium Homeostasis

By influencing Ca²⁺ homeostasis in spatially and architecturally distinct neuronal compartments, the endoplasmic reticulum (ER) illustrates the notion that form and function are intimately related. The contribution of ER to neuronal Ca²⁺ homeostasis is attributed to the organelle being the largest reservoir of intracellular Ca²⁺ and having a high density of Ca²⁺ channels and transporters. As such, ER Ca²⁺ has incontrovertible roles in the regulation of axodendritic growth and morphology, synaptic vesicle release, and neural activity dependent gene expression, synaptic plasticity, and mitochondrial bioenergetics. Not surprisingly, many neurological diseases arise from ER Ca²⁺ dyshomeostasis, either directly due to alterations in ER resident proteins, or indirectly via processes that are coupled to the regulators of ER Ca²⁺ dynamics. In this review, we describe the mechanisms involved in the establishment of ER Ca²⁺ homeostasis in neurons. We elaborate upon how changes in the spatiotemporal dynamics of Ca²⁺ exchange between the ER and other organelles sculpt neuronal function and provide examples that demonstrate the involvement of ER Ca²⁺ dyshomeostasis in a range of neurological and neurodegenerative diseases.

Geometric principles of second messenger dynamics in dendritic spines

Dendritic spines are small, bulbous protrusions along dendrites in neurons and play a critical role in synaptic transmission. Dendritic spines come in a variety of shapes that depend on their developmental state. Additionally, roughly 14-19% of mature spines have a specialized endoplasmic reticulum called the spine apparatus. How does the shape of a postsynaptic spine and its internal organization affect the spatio-temporal dynamics of short timescale signaling? Answers to this question are central to our understanding the initiation of synaptic transmission, learning, and memory formation. In this work, we investigated the effect of spine and spine apparatus size and shape on the spatio-temporal dynamics of second messengers using mathematical modeling using reaction-diffusion equations in idealized geometries (ellipsoids, spheres, and mushroom-shaped). Our analyses and simulations showed that in the short timescale, spine size and shape coupled with the spine apparatus geometries govern the spatiotemporal dynamics of second messengers. We show that the curvature of the geometries gives rise to pseudo-harmonic functions, which predict the locations of maximum and minimum concentrations along the spine head. Furthermore, we showed that the lifetime of the concentration gradient can be fine-tuned by localization of fluxes on the spine head and varying the relative curvatures and distances between the spine apparatus and the spine head. Thus, we have identified several key geometric determinants of how the spine head and spine apparatus may regulate the short timescale chemical dynamics of small molecules that control synaptic plasticity.

How dendritic spines shape calcium dynamics

JGP study develops mathematical model that describes how calcium signaling could be influenced by spine geometry and ultrastructure.