Paradoxical signaling regulates structural plasticity in dendritic spines

Spatiotemporal orchestration of calcium-cAMP oscillations on AKAP/AC nanodomains is governed by an incoherent feedforward loop

The nanoscale organization of enzymes associated with the dynamics of second messengers is critical for ensuring compartmentation and localization of signaling molecules in cells. Specifically, the spatiotemporal orchestration of cAMP and Ca2+ oscillations is critical for many cellular functions. Previous experimental studies have shown that the formation of nanodomains of A-kinase anchoring protein 79/150 (AKAP150) and adenylyl cyclase 8 (AC8) on the surface of pancreatic MIN6 β cells modulates the phase of Ca2+-cAMP oscillations from out-of-phase to in-phase. In this work, we develop computational models of the Ca2+/cAMP pathway and AKAP/AC nanodomain formation that give rise to the two important predictions: instead of an arbitrary phase difference, the out-of-phase Ca2+/cAMP oscillation reaches Ca2+ trough and cAMP peak simultaneously, which is defined as inversely out-of-phase; the in-phase and inversely out-of-phase oscillations associated with Ca2+-cAMP dynamics on and away from the nanodomains can be explained by an incoherent feedforward loop. Factors such as cellular surface-to-volume ratio, compartment size, and distance between nanodomains do not affect the existence of in-phase or inversely out-of-phase Ca2+/cAMP oscillation, but cellular surface-to-volume ratio and compartment size can affect the time delay for the inversely out-of-phase Ca2+/cAMP oscillation while the distance between two nanodomains does not. Finally, we predict that both the Turing pattern-generated nanodomains and experimentally measured nanodomains demonstrate the existence of in-phase and inversely out-of-phase Ca2+/cAMP oscillation when the AC8 is at a low level, consistent with the behavior of an incoherent feedforward loop. These findings unveil the key circuit motif that governs cAMP and Ca2+ oscillations and advance our understanding of how nanodomains can lead to spatial compartmentation of second messengers.

Hub stability in the calcium calmodulin-dependent protein kinase II

The calcium calmodulin protein kinase II (CaMKII) is a multi-subunit ring assembly with a central hub formed by the association domains. There is evidence for hub polymorphism between and within CaMKII isoforms, but the link between polymorphism and subunit exchange has not been resolved. Here, we present near-atomic resolution cryogenic electron microscopy (cryo-EM) structures revealing that hubs from the α and β isoforms, either standalone or within an β holoenzyme, coexist as 12 and 14 subunit assemblies. Single-molecule fluorescence microscopy of Venus-tagged holoenzymes detects intermediate assemblies and progressive dimer loss due to intrinsic holoenzyme lability, and holoenzyme disassembly into dimers upon mutagenesis of a conserved inter-domain contact. Molecular dynamics (MD) simulations show the flexibility of 4-subunit precursors, extracted in-silico from the β hub polymorphs, encompassing the curvature of both polymorphs. The MD explains how an open hub structure also obtained from the β holoenzyme sample could be created by dimer loss and analysis of its cryo-EM dataset reveals how the gap could open further. An assembly model, considering dimer concentration dependence and strain differences between polymorphs, proposes a mechanism for intrinsic hub lability to fine-tune the stoichiometry of αβ heterooligomers for their dynamic localization within synapses in neurons.

Real-time single-molecule imaging of CaMKII-calmodulin interactions

The binding of calcium/calmodulin (CAM) to calcium/calmodulin-dependent protein kinase II (CaMKII) initiates an ATP-driven cascade that triggers CaMKII autophosphorylation. The autophosphorylation in turn increases the CaMKII affinity for CAM. Here, we studied the ATP dependence of CAM association with the actin-binding CaMKIIβ isoform using single-molecule total internal reflection fluorescence microscopy. Rhodamine-CAM associations/dissociations to surface-immobilized Venus-CaMKIIβ were resolved with 0.5 s resolution from video records, batch-processed with a custom algorithm. CAM occupancy was determined simultaneously with spot-photobleaching measurement of CaMKII holoenzyme stoichiometry. We show the ATP-dependent increase of the CAM association requires dimer formation for both the α and β isoforms. The study of mutant β holoenzymes revealed that the ATP-dependent increase in CAM affinity results in two distinct states. The phosphorylation-defective (T287.306-307A) holoenzyme resides only in the low-affinity state. CAM association is further reduced in the T287A holoenzyme relative to T287.306-307A. In the absence of ATP, the affinity of CAM for the T287.306-307A mutant and the wild-type monomer are comparable. The affinity of the ATP-binding impaired (K43R) mutant is even weaker. In ATP, the K43R holoenzyme resides in the low-affinity state. The phosphomimetic mutant (T287D) resides only in a 1000-fold higher-affinity state, with mean CAM occupancy of more than half of the 14-mer holoenzyme stoichiometry in picomolar CAM. ATP promotes T287D holoenzyme disassembly but does not elevate CAM occupancy. Single Poisson distributions characterized the ATP-dependent CAM occupancy of mutant holoenzymes. In contrast, the CAM occupancy of the wild-type population had a two-state distribution with both low- and high-affinity states represented. The low-affinity state was the dominant state, a result different from published in vitro assays. Differences in assay conditions can alter the balance between activating and inhibitory autophosphorylation. Bound ATP could be sufficient for CaMKII structural function, while antagonistic autophosphorylations may tune CaMKII kinase-regulated action-potential frequency decoding in vivo.

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.

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.

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.

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.

Mechanisms underlying divergent relationships between Ca2+ and YAP/TAZ signalling

Yes-associated protein (YAP) and its homologue TAZ are transducers of several biochemical and biomechanical signals, integrating multiplexed inputs from the microenvironment into higher level cellular functions such as proliferation, differentiation and migration. Emerging evidence suggests that Ca2+ is a key second messenger that connects microenvironmental input signals and YAP/TAZ regulation. However, studies that directly modulate Ca2+ have reported contradictory YAP/TAZ responses: in some studies, a reduction in Ca2+ influx increases the activity of YAP/TAZ, while in others, an increase in Ca2+ influx activates YAP/TAZ. Importantly, Ca2+ and YAP/TAZ exhibit distinct spatiotemporal dynamics, making it difficult to unravel their connections from a purely experimental approach. In this study, we developed a network model of Ca2+ -mediated YAP/TAZ signalling to investigate how temporal dynamics and crosstalk of signalling pathways interacting with Ca2+ can alter the YAP/TAZ response, as observed in experiments. By including six signalling modules (e.g. GPCR, IP3-Ca2+ , kinases, RhoA, F-actin and Hippo-YAP/TAZ) that interact with Ca2+ , we investigated both transient and steady-state cell response to angiotensin II and thapsigargin stimuli. The model predicts that stimuli, Ca2+ transients and frequency-dependent relationships between Ca2+ and YAP/TAZ are primarily mediated by cPKC, DAG, CaMKII and F-actin. Simulation results illustrate the role of Ca2+ dynamics and CaMKII bistable response in switching the direction of changes in Ca2+ -induced YAP/TAZ activity. A frequency-dependent YAP/TAZ response revealed the competition between upstream regulators of LATS1/2, leading to the YAP/TAZ non-monotonic response to periodic GPCR stimulation. This study provides new insights into underlying mechanisms responsible for the controversial Ca2+ -YAP/TAZ relationship observed in experiments. KEY POINTS: YAP/TAZ integrates biochemical and biomechanical inputs to regulate cellular functions, and Ca2+ acts as a key second messenger linking cellular inputs to YAP/TAZ. Studies have reported contradictory Ca2+ -YAP/TAZ relationships for different cell types and stimuli. A network model of Ca2+ -mediated YAP/TAZ signalling was developed to investigate the underlying mechanisms of divergent Ca2+ -YAP/TAZ relationships. The model predicts context-dependent Ca2+ transient, CaMKII bistable response and frequency-dependent activation of LATS1/2 upstream regulators as mechanisms governing the Ca2+ -YAP/TAZ relationship. This study provides new insights into the underlying mechanisms of the controversial Ca2+ -YAP/TAZ relationship to better understand the dynamics of cellular functions controlled by YAP/TAZ activity.

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.

Dendritic Spines: Synaptogenesis and Synaptic Pruning for the Developmental Organization of Brain Circuits

Synaptic overproduction and elimination is a regular developmental event in the mammalian brain. In the cerebral cortex, synaptic overproduction is almost exclusively correlated with glutamatergic synapses located on dendritic spines. Therefore, analysis of changes in spine density on different parts of the dendritic tree in identified classes of principal neurons could provide insight into developmental reorganization of specific microcircuits.The activity-dependent stabilization and selective elimination of the initially overproduced synapses is a major mechanism for generating diversity of neural connections beyond their genetic determination. The largest number of overproduced synapses was found in the monkey and human cerebral cortex. The highest (exceeding adult values by two- to threefold) and most protracted overproduction (up to third decade of life) was described for associative layer IIIC pyramidal neurons in the human dorsolateral prefrontal cortex.Therefore, the highest proportion and extraordinarily extended phase of synaptic spine overproduction is a hallmark of neural circuitry in human higher-order associative areas. This indicates that microcircuits processing the most complex human cognitive functions have the highest level of developmental plasticity. This finding is the backbone for understanding the effect of environmental impact on the development of the most complex, human-specific cognitive and emotional capacities, and on the late onset of human-specific neuropsychiatric disorders, such as autism and schizophrenia.

Activation of NMDA receptors in brain endothelial cells increases transcellular permeability

Neurovascular coupling is a precise mechanism that induces increased blood flow to activated brain regions, thereby providing oxygen and glucose. In this study, we hypothesized that N-methyl-D-aspartate (NMDA) receptor signaling, the most well characterized neurotransmitter signaling system which regulates delivery of essential molecules through the blood–brain barrier (BBB). Upon application of NMDA in both in vitro and in vivo models, increased delivery of bioactive molecules that was mediated through modulation of molecules involved in molecular delivery, including clathrin and caveolin were observed. Also, NMDA activation induced structural changes in the BBB and increased transcellular permeability that showed regional heterogeneity in its responses. Moreover, NMDA receptor activation increased endosomal trafficking and facilitated inactivation of lysosomal pathways and consequently increased molecular delivery mediated by activation of calmodulin-dependent protein kinase II (CaMKII) and RhoA/protein kinase C (PKC). Subsequent in vivo experiments using mice specifically lacking NMDA receptor subunit 1 in endothelial cells showed decreased neuronal density in the brain cortex, suggesting that a deficiency in NMDA receptor signaling in brain endothelial cells induces neuronal losses. Together, these results highlight the importance of NMDA-receptor-mediated signaling in the regulation of BBB permeability that surprisingly also affected CD31 staining.

Dynamics and Sensitivity of Signaling Pathways

Purpose of Review

Signaling pathways serve to communicate information about extracellular conditions into the cell, to both the nucleus and cytoplasmic processes to control cell responses. Genetic mutations in signaling network components are frequently associated with cancer and can result in cells acquiring an ability to divide and grow uncontrollably. Because signaling pathways play such a significant role in cancer initiation and advancement, their constituent proteins are attractive therapeutic targets. In this review, we discuss how signaling pathway modeling can assist with identifying effective drugs for treating diseases, such as cancer. An achievement that would facilitate the use of such models is their ability to identify controlling biochemical parameters in signaling pathways, such as molecular abundances and chemical reaction rates, because this would help determine effective points of attack by therapeutics.

Recent Findings

We summarize the current state of understanding the sensitivity of phosphorylation cycles with and without sequestration. We also describe some basic properties of regulatory motifs including feedback and feedforward regulation.

Summary

Although much recent work has focused on understanding the dynamics and particularly the sensitivity of signaling networks in eukaryotic systems, there is still an urgent need to build more scalable models of signaling networks that can appropriately represent their complexity across different cell types and tumors.

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.

β-Arrestin2 Is Critically Involved in the Differential Regulation of Phosphosignaling Pathways by Thyrotropin-Releasing Hormone and Taltirelin

In recent years, thyrotropin-releasing hormone (TRH) and its analogs, including taltirelin (TAL), have demonstrated a range of effects on the central nervous system that represent potential therapeutic agents for the treatment of various neurological disorders, including neurodegenerative diseases. However, the molecular mechanisms of their actions remain poorly understood. In this study, we investigated phosphosignaling dynamics in pituitary GH1 cells affected by TRH and TAL and the putative role of β-arrestin2 in mediating these effects. Our results revealed widespread alterations in many phosphosignaling pathways involving signal transduction via small GTPases, MAP kinases, Ser/Thr- and Tyr-protein kinases, Wnt/β-catenin, and members of the Hippo pathway. The differential TRH- or TAL-induced phosphorylation of numerous proteins suggests that these ligands exhibit some degree of biased agonism at the TRH receptor. The different phosphorylation patterns induced by TRH or TAL in β-arrestin2-deficient cells suggest that the β-arrestin2 scaffold is a key factor determining phosphorylation events after TRH receptor activation. Our results suggest that compounds that modulate kinase and phosphatase activity can be considered as additional adjuvants to enhance the potential therapeutic value of TRH or TAL.

Oxidative stress and Rho GTPases in the biogenesis of tunnelling nanotubes: implications in disease and therapy

Tunnelling nanotubes (TNTs) are an emerging route of long-range intercellular communication that mediate cell-to-cell exchange of cargo and organelles and contribute to maintaining cellular homeostasis by balancing diverse cellular stresses. Besides their role in intercellular communication, TNTs are implicated in several ways in health and disease. Transfer of pathogenic molecules or structures via TNTs can promote the progression of neurodegenerative diseases, cancer malignancy, and the spread of viral infection. Additionally, TNTs contribute to acquiring resistance to cancer therapy, probably via their ability to rescue cells by ameliorating various pathological stresses, such as oxidative stress, reactive oxygen species (ROS), mitochondrial dysfunction, and apoptotic stress. Moreover, mesenchymal stem cells play a crucial role in the rejuvenation of targeted cells with mitochondrial heteroplasmy and oxidative stress by transferring healthy mitochondria through TNTs. Recent research has focussed on uncovering the key regulatory molecules involved in the biogenesis of TNTs. However further work will be required to provide detailed understanding of TNT regulation. In this review, we discuss possible associations with Rho GTPases linked to oxidative stress and apoptotic signals in biogenesis pathways of TNTs and summarize how intercellular trafficking of cargo and organelles, including mitochondria, via TNTs plays a crucial role in disease progression and also in rejuvenation/therapy.

Computation, wiring, and plasticity in synaptic clusters

Synaptic clusters on dendrites are extraordinarily compact computational building blocks. They contribute to key local computations through biophysical and biochemical signaling that utilizes convergence in space and time as an organizing principle. However, these computations can only arise in very special contexts. Dendritic cluster computations, their highly organized input connectivity, and the mechanisms for their formation are closely linked, yet these have not been analyzed as parts of a single process. Here, we examine these linkages. The sheer density of axonal and dendritic arborizations means that there are far more potential connections (close enough for a spine to reach an axon) than actual ones. We see how dendritic clusters draw upon electrical, chemical, and mechano-chemical signaling to implement the rules for formation of connections and subsequent computations. Crucially, the same mechanisms that underlie their functions also underlie their formation.

Temporal pattern and synergy influence activity of ERK signaling pathways during L-LTP induction

Long-lasting long-term potentiation (L-LTP) is a cellular mechanism of learning and memory storage. Studies have demonstrated a requirement for extracellular signal-regulated kinase (ERK) activation in L-LTP produced by a diversity of temporal stimulation patterns. Multiple signaling pathways converge to activate ERK, with different pathways being required for different stimulation patterns. To answer whether and how different temporal patterns select different signaling pathways for ERK activation, we developed a computational model of five signaling pathways (including two novel pathways) leading to ERK activation during L-LTP induction. We show that calcium and cAMP work synergistically to activate ERK and that stimuli given with large intertrial intervals activate more ERK than shorter intervals. Furthermore, these pathways contribute to different dynamics of ERK activation. These results suggest that signaling pathways with different temporal sensitivities facilitate ERK activation to diversity of temporal patterns.

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.

Zc3h10 regulates adipogenesis by controlling translation and F-actin/mitochondria interaction

The commitment of mesenchymal stem cells to preadipocytes is stimulated by hormonal induction. Preadipocytes induced to differentiate repress protein synthesis, remodel their cytoskeleton, and increase mitochondrial function to support anabolic pathways. These changes enable differentiation into mature adipocytes. Our understanding of the factors that coordinately regulate the early events of adipocyte differentiation remains incomplete. Here, by using multipronged approaches, we have identified zinc finger CCCH-type containing 10 (Zc3h10) as a critical regulator of the early stages of adipogenesis. Zc3h10 depletion in preadipocytes resulted in increased protein translation and impaired filamentous (F)-actin remodeling, with the latter detrimental effect leading to mitochondrial and metabolic dysfunction. These defects negatively affected differentiation to mature adipocytes. In contrast, Zc3h10 overexpression yielded mature adipocytes with remarkably increased lipid droplet size. Overall, our study establishes Zc3h10 as a fundamental proadipogenic transcription factor that represses protein synthesis and promotes F-actin/mitochondria dynamics to ensure proper energy metabolism and favor lipid accumulation.

Quantifying the roles of space and stochasticity in computer simulations for cell biology and cellular biochemistry

Most of the fascinating phenomena studied in cell biology emerge from interactions among highly organized multimolecular structures embedded into complex and frequently dynamic cellular morphologies. For the exploration of such systems, computer simulation has proved to be an invaluable tool, and many researchers in this field have developed sophisticated computational models for application to specific cell biological questions. However, it is often difficult to reconcile conflicting computational results that use different approaches to describe the same phenomenon. To address this issue systematically, we have defined a series of computational test cases ranging from very simple to moderately complex, varying key features of dimensionality, reaction type, reaction speed, crowding, and cell size. We then quantified how explicit spatial and/or stochastic implementations alter outcomes, even when all methods use the same reaction network, rates, and concentrations. For simple cases, we generally find minor differences in solutions of the same problem. However, we observe increasing discordance as the effects of localization, dimensionality reduction, and irreversible enzymatic reactions are combined. We discuss the strengths and limitations of commonly used computational approaches for exploring cell biological questions and provide a framework for decision making by researchers developing new models. As computational power and speed continue to increase at a remarkable rate, the dream of a fully comprehensive computational model of a living cell may be drawing closer to reality, but our analysis demonstrates that it will be crucial to evaluate the accuracy of such models critically and systematically.

Functional repertoire of protein kinases and phosphatases in synaptic plasticity and associated neurological disorders

Protein phosphorylation and dephosphorylation are two essential and vital cellular mechanisms that regulate many receptors and enzymes through kinases and phosphatases. Ca²⁺- dependent kinases and phosphatases are responsible for controlling neuronal processing; balance is achieved through opposition. During molecular mechanisms of learning and memory, kinases generally modulate positively while phosphatases modulate negatively. This review outlines some of the critical physiological and structural aspects of kinases and phosphatases involved in maintaining postsynaptic structural plasticity. It also explores the link between neuronal disorders and the deregulation of phosphatases and kinases.

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.

Unique cellular protrusions mediate breast cancer cell migration by tethering to osteogenic cells

Migration and invasion are key properties of metastatic cancer cells. These properties can be acquired through intrinsic reprogramming processes such as epithelial-mesenchymal transition. In this study, we discovered an alternative "migration-by-tethering" mechanism through which cancer cells gain the momentum to migrate by adhering to mesenchymal stem cells or osteoblasts. This tethering is mediated by both heterotypic adherens junctions and gap junctions, and leads to a unique cellular protrusion supported by cofilin-coated actin filaments. Inhibition of gap junctions or depletion of cofilin reduces migration-by-tethering. We observed evidence of these protrusions in bone segments harboring experimental and spontaneous bone metastasis in animal models. These data exemplify how cancer cells may acquire migratory ability without intrinsic reprogramming. Furthermore, given the important roles of osteogenic cells in early-stage bone colonization, our observations raise the possibility that migration-by-tethering may drive the relocation of disseminated tumor cells between different niches in the bone microenvironment.

Interactions between calmodulin and neurogranin govern the dynamics of CaMKII as a leaky integrator

Calmodulin-dependent kinase II (CaMKII) has long been known to play an important role in learning and memory as well as long term potentiation (LTP). More recently it has been suggested that it might be involved in the time averaging of synaptic signals, which can then lead to the high precision of information stored at a single synapse. However, the role of the scaffolding molecule, neurogranin (Ng), in governing the dynamics of CaMKII is not yet fully understood. In this work, we adopt a rule-based modeling approach through the Monte Carlo method to study the effect of Ca2+ signals on the dynamics of CaMKII phosphorylation in the postsynaptic density (PSD). Calcium surges are observed in synaptic spines during an EPSP and back-propagating action potential due to the opening of NMDA receptors and voltage dependent calcium channels. Using agent-based models, we computationally investigate the dynamics of phosphorylation of CaMKII monomers and dodecameric holoenzymes. The scaffolding molecule, Ng, when present in significant concentration, limits the availability of free calmodulin (CaM), the protein which activates CaMKII in the presence of calcium. We show that Ng plays an important modulatory role in CaMKII phosphorylation following a surge of high calcium concentration. We find a non-intuitive dependence of this effect on CaM concentration that results from the different affinities of CaM for CaMKII depending on the number of calcium ions bound to the former. It has been shown previously that in the absence of phosphatase, CaMKII monomers integrate over Ca2+ signals of certain frequencies through autophosphorylation (Pepke et al, Plos Comp. Bio., 2010). We also study the effect of multiple calcium spikes on CaMKII holoenzyme autophosphorylation, and show that in the presence of phosphatase, CaMKII behaves as a leaky integrator of calcium signals, a result that has been recently observed in vivo. Our models predict that the parameters of this leaky integrator are finely tuned through the interactions of Ng, CaM, CaMKII, and PP1, providing a mechanism to precisely control the sensitivity of synapses to calcium signals. Author Summary not valid for PLOS ONE submissions.

The Mixture of Autoregressive Hidden Markov Models of Morphology for Dentritic Spines During Activation Process

The dendritic spines play a crucial role in learning and memory processes, epileptogenesis, drug addiction, and postinjury recovery. The shape of the dendritic spine is a morphological key to understand learning and memory process. The classification of the dendritic spines is based on their shapes but the major questions are how the shapes changes in time, how the synaptic strength changes, and is there a correlation between shapes and synaptic strength? Because the changes of the classes by dendritic spines during activation are time dependent, the forward-directed autoregressive hidden Markov model (ARHMM) can be used to model these changes. It is also more appropriate to use an ARHMM directed backward in time. Thus, the mixture of forward-directed ARHMM and backward-directed ARHMM (MARHMM) is used to model time-dependent data related to the dendritic spines. In this article, we discuss (1) how to choose the initial probability vector and transition and dependence matrices in ARHMM and MARHMM for modeling the dendritic spines changes and (2) how to estimate these matrices. Many descriptors to classify dendritic spines in two-dimensional or/and three-dimensional (3D) are available. Our results from sensitivity analysis show that the classification that comes from 3D descriptors is closer to the truth, and estimated transition and dependence probability matrices are connected with the molecular mechanism of the dendritic spines activation.

Ca2+ signaling in T lymphocytes: the interplay of the endoplasmic reticulum, mitochondria, membrane potential, and CRAC channels on transcription factor activation

T cell receptor stimulation initiates a cascade of reactions that cause an increase in intracellular calcium (Ca2+) concentration mediated through inositol 1,4,5-trisphosphate (IP3). To understand the basic mechanisms by which the immune response in T cells is activated, it is useful to understand the signaling pathways that contain important targets for drugs in a quantitative fashion. A computational model helps us to understand how the selected elements in the pathways interact with each other, and which component plays the crucial role in systems. We have developed a mathematical model to explore the mechanism for controlling transcription factor activity, which regulates gene expression, by the modulation of calcium signaling triggered during T cell activation. The model simulates the activation and modulation of Ca2+ release-activated Ca2+ (CRAC) channels by mitochondrial dynamics and depletion of endoplasmic reticulum (ER) store, and also includes membrane potential in T-cells. The model simulates the experimental finding that increases in Ca2+ current enhances the activation of transcription factors and the Ca2+ influx through CRAC is also essential for the NFAT and NFκB activation. The model also suggests that plasma membrane Ca2+-ATPase (PMCA) controls a majority of the extrusion of Ca2+ and modulates the activation of CRAC channels. Furthermore, the model simulations explain how the complex interaction of the endoplasmic reticulum, membrane potential, mitochondria, and ion channels such as CRAC channels control T cell activation.

Interplay of miR-137 and EZH2 contributes to the genome-wide redistribution of H3K27me3 underlying the Pb-induced memory impairment

Compromised learning and memory is a common feature of multiple neurodegenerative disorders. A paradigm spatial memory impairment could be caused by developmental lead (Pb) exposure. Growing evidence implicates epigenetic modifications in the Pb-mediated memory deficits; however, how histone modifications exemplified by H3K27me3 (H3 Lys27 trimethylation) contribute to this pathogenesis remains poorly understood. Here we found that Pb exposure diminished H3K27me3 levels in vivo by suppressing EZH2 (enhancer of zeste homolog 2) expression at an early stage. EZH2 overexpression in Pb-treated rats rescued the H3K27me3 abundance and partially restored the normal spatial memory, as manifested by the rat performance in a Morris water maze test, and structural analysis of hippocampal spine densities. Furthermore, miR-137 and EZH2 constitute mutually inhibitory loop to regulate the H3K27me3 level, and this feedback regulation could be specifically activated by Pb treatment. Considering genes targeted by H3K27me3, ChIP-chip (chromatin immunoprecipitation on chip) studies revealed that Pb could remodel the genome-wide distribution of H3K27me3, represented by pathways like transcriptional regulation, developmental regulation, cell motion, and apoptosis, as well as a novel Wnt9b locus. As a Wnt isoform associated with canonical and noncanonical signaling, Wnt9b was regulated by the opposite modifications of H3K4me3 (H3 Lys4 trimethylation) and H3K27me3 in Pb-exposed neurons. Rescue trials further validated the contribution of Wnt9b to Pb-induced neuronal impairments, wherein canonical or noncanonical Wnt signaling potentially exhibited destructive or protective roles, respectively. In summary, the study reveals an epigenetic-based molecular change underlying Pb-triggered spatial memory deficits, and provides new potential avenues for our understanding of neurodegenerative diseases with environmental etiology.

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.

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

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

Acute slice preparation for electrophysiology increases spine numbers equivalently in the male and female juvenile hippocampus: a DiI labeling study

Hippocampal slices are widely used for in vitro electrophysiological experiments to study underlying mechanisms for synaptic transmission and plasticity, and there is a growing appreciation for sex differences in synaptic plasticity. To date, several studies have shown that the process of making slices from male animals can induce synaptogenesis in cornu ammonis area 1 (CA1) pyramidal cells, but there is a paucity of data for females and other brain regions. In the current study we use microcrystals of the lipophilic carbocyanine dye DiI (1,1'-dioctadecyl-3,3,3',3'-tetramethylindocarbocyanine perchlorate) to stain individual neurons in the CA1 and dentate gyrus (DG) hippocampal subfields of postnatal day 21 male and female rats. We show that the preparation of sections for electrophysiology produces significant increases in spines in sections obtained from females, similar to that observed in males. We also show that the procedures used for in vitro electrophysiology also result in significant spine increases in the DG and CA1 subfields. These results demonstrate the utility of this refined DiI procedure for staining neuronal dendrites and spines. They also show, for the first time, that in vitro electrophysiology slice preparations enhance spine numbers on hippocampal cells equivalently in both juvenile females and males.NEW & NOTEWORTHY This study introduces a new DiI technique that elucidates differences in spine numbers in juvenile female and male hippocampus, and shows that slice preparations for hippocampal electrophysiology in vitro may mask these differences.

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

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

Architectural Dynamics of CaMKII-Actin Networks

Calcium-calmodulin-dependent kinase II (CaMKII) has an important role in dendritic spine remodeling upon synaptic stimulation. Using fluorescence video microscopy and image analysis, we investigated the architectural dynamics of rhodamine-phalloidin stabilized filamentous actin (F-actin) networks cross-linked by CaMKII. We used automated image analysis to identify F-actin bundles and crossover junctions and developed a dimensionless metric to characterize network architecture. Similar networks were formed by three different CaMKII species with a 10-fold length difference in the linker region between the kinase domain and holoenzyme hub, implying linker length is not a primary determinant of F-actin cross-linking. Electron micrographs showed that at physiological molar ratios, single CaMKII holoenzymes cross-linked multiple F-actin filaments at random, whereas at higher CaMKII/F-actin ratios, filaments bundled. Light microscopy established that the random network architecture resisted macromolecular crowding with polyethylene glycol and blocked ATP-powered compaction by myosin-II miniature filaments. Importantly, the networks disassembled after the addition of calcium-calmodulin and were then spaced within 3 min into compacted foci by myosin motors or more slowly (30 min) aggregated by crowding. Single-molecule total internal reflection fluorescence microscopy showed CaMKII dissociation from surface-immobilized globular actin exhibited a monoexponential dwell-time distribution, whereas CaMKII bound to F-actin networks had a long-lived fraction, trapped at crossover junctions. Release of CaMKII from F-actin, triggered by calcium-calmodulin, was too rapid to measure with flow-cell exchange (<20 s). The residual bound fraction was reduced substantially upon addition of an N-methyl-D-aspartate receptor peptide analog but not ATP. These results provide mechanistic insights to CaMKII-actin interactions at the collective network and single-molecule level. Our findings argue that CaMKII-actin networks in dendritic spines maintain spine size against physical stress. Upon synaptic stimulation, CaMKII is disengaged by calcium-calmodulin, triggering network disassembly, expansion, and subsequent compaction by myosin motors with kinetics compatible with the times recorded for the poststimulus changes in spine volume.

Systems biology of cellular membranes: a convergence with biophysics

Systems biology and systems medicine have played an important role in the last two decades in shaping our understanding of biological processes. While systems biology is synonymous with network maps and '-omics' approaches, it is not often associated with mechanical processes. Here, we make the case for considering the mechanical and geometrical aspects of biological membranes as a key step in pushing the frontiers of systems biology of cellular membranes forward. We begin by introducing the basic components of cellular membranes, and highlight their dynamical aspects. We then survey the functions of the plasma membrane and the endomembrane system in signaling, and discuss the role and origin of membrane curvature in these diverse cellular processes. We further give an overview of the experimental and modeling approaches to study membrane phenomena. We close with a perspective on the converging futures of systems biology and membrane biophysics, invoking the need to include physical variables such as location and geometry in the study of cellular membranes. WIREs Syst Biol Med 2017, 9:e1386. doi: 10.1002/wsbm.1386 For further resources related to this article, please visit the WIREs website.

Applying Pattern Recognition to High-Resolution Images to Determine Cellular Signaling Status

Two frequently used tools to acquire high- resolution images of cells are scanning electron microscopy (SEM) and atomic force microscopy (AFM). The former provides a nanometer resolution view of cellular features rapidly and with high throughput, while the latter enables visualizing hydrated and living cells. In current practice, these images are viewed by eye to determine cellular status, e.g., activated versus resting. Automatic and quantitative data analysis is lacking. This paper develops an algorithm of pattern recognition that works very effectively for AFM and SEM images. Using rat basophilic leukemia cells, our approach creates a support vector machine to automatically classify resting and activated cells. Ten-fold cross-validation with cells that are known to be activated or resting gives a good estimate of the generalized classification results. The pattern recognition of AFM images achieves 100% accuracy, while SEM reaches 95.4% for our images as well as images published in prior literature. This outcome suggests that our methodology could become an important and frequently used tool for researchers utilizing AFM and SEM for structural characterization as well as determining cellular signaling status and function.

Stability analysis in spatial modeling of cell signaling

Advances in high-resolution microscopy and other techniques have emphasized the spatio-temporal nature of information transfer through signal transduction pathways. The compartmentalization of signaling molecules and the existence of microdomains are now widely acknowledged as key features in biochemical signaling. To complement experimental observations of spatio-temporal dynamics, mathematical modeling has emerged as a powerful tool. Using modeling, one can not only recapitulate experimentally observed dynamics of signaling molecules, but also gain an understanding of the underlying mechanisms in order to generate experimentally testable predictions. Reaction-diffusion systems are commonly used to this end; however, the analysis of coupled nonlinear systems of partial differential equations, generated by considering large reaction networks is often challenging. Here, we aim to provide an introductory tutorial for the application of reaction-diffusion models to the spatio-temporal dynamics of signaling pathways. In particular, we outline the steps for stability analysis of such models, with a focus on biochemical signal transduction. WIREs Syst Biol Med 2018, 10:e1395. doi: 10.1002/wsbm.1395 This article is categorized under: Biological Mechanisms > Cell Signaling Analytical and Computational Methods > Dynamical Methods Models of Systems Properties and Processes > Mechanistic Models.