Signaling In Dendritic Spines Research Articles

Dynamic Network Connectivity: from monkeys to humans.

Human brain imaging research using functional MRI (fMRI) has uncovered flexible variations in the functional connectivity between brain regions. While some of this variability likely arises from the pattern of information flow through circuits, it may also be influenced by rapid changes in effective synaptic strength at the molecular level, a phenomenon called Dynamic Network Connectivity (DNC) discovered in non-human primate circuits. These neuromodulatory molecular mechanisms are found in layer III of the macaque dorsolateral prefrontal cortex (dlPFC), the site of the microcircuits shown by Goldman-Rakic to be critical for working memory. This research has shown that the neuromodulators acetylcholine, norepinephrine, and dopamine can rapidly change the strength of synaptic connections in layer III dlPFC by (1) modifying the depolarization state of the post-synaptic density needed for NMDA receptor neurotransmission and (2) altering the open state of nearby potassium channels to rapidly weaken or strengthen synaptic efficacy and the strength of persistent neuronal firing. Many of these actions involve increased cAMP-calcium signaling in dendritic spines, where varying levels can coordinate the arousal state with the cognitive state. The current review examines the hypothesis that some of the dynamic changes in correlative strength between cortical regions observed in human fMRI studies may arise from these molecular underpinnings, as has been seen when pharmacological agents or genetic alterations alter the functional connectivity of the dlPFC consistent with the macaque physiology. These DNC mechanisms provide essential flexibility but may also confer vulnerability to malfunction when dysregulated in cognitive disorders.

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.

RGS14 limits seizure-induced mitochondrial oxidative stress and pathology in hippocampus

RGS14 is a complex multifunctional scaffolding protein that is highly enriched within pyramidal cells (PCs) of hippocampal area CA2. In these neurons, RGS14 suppresses glutamate-induced calcium influx and related G protein and ERK signaling in dendritic spines to restrain postsynaptic signaling and plasticity. Previous findings show that, unlike PCs of hippocampal areas CA1 and CA3, CA2 PCs are resistant to a number of neurological insults, including degeneration caused by temporal lobe epilepsy (TLE). While RGS14 is protective against peripheral injury, similar roles for RGS14 during pathological injury in hippocampus remain unexplored. Recent studies showed that area CA2 modulates hippocampal excitability, generates epileptiform activity and promotes hippocampal pathology in animal models and patients with TLE. Because RGS14 suppresses CA2 excitability and signaling, we hypothesized that RGS14 would moderate seizure behavior and early hippocampal pathology following seizure activity, possibly affording protection to CA2 PCs. Using kainic acid (KA) to induce status epilepticus (KA-SE) in mice, we show that the loss of RGS14 (RGS14 KO) accelerated onset of limbic motor seizures and mortality compared to wild type (WT) mice, and that KA-SE upregulated RGS14 protein expression in CA2 and CA1 PCs of WT. Our proteomics data show that the loss of RGS14 impacted the expression of a number of proteins at baseline and after KA-SE, many of which associated unexpectedly with mitochondrial function and oxidative stress. RGS14 was shown to localize to the mitochondria in CA2 PCs of mice and reduce mitochondrial respiration in vitro. As a readout of oxidative stress, we found that RGS14 KO dramatically increased 3- nitrotyrosine levels in CA2 PCs, which was greatly exacerbated following KA-SE and correlated with a lack of superoxide dismutase 2 (SOD2) induction. Assessing for hallmarks of seizure pathology in RGS14 KO, we unexpectedly found no differences in neuronal injury in CA2 PCs. However, we observed a striking and surprising lack of microgliosis in CA1 and CA2 of RGS14 KO compared to WT. Together, our data demonstrate a newly appreciated role for RGS14 in limiting intense seizure activity and pathology in hippocampus. Our findings are consistent with a model where RGS14 limits seizure onset and mortality and, after seizure, is upregulated to support mitochondrial function, prevent oxidative stress in CA2 PCs, and promote microglial activation in hippocampus.

Fast Synaptically Activated Calcium and Sodium Kinetics in Hippocampal Pyramidal Neuron Dendritic Spines.

An accurate assessment of the time course, components, and magnitude of postsynaptic currents is important for a quantitative understanding of synaptic integration and signaling in dendritic spines. These parameters have been studied in some detail in previous experiments, primarily using two-photon imaging of [Ca2+]i changes and two-photon uncaging of glutamate. However, even with these revolutionary techniques, there are some missing pieces in our current understanding, particularly related to the time courses of synaptically evoked [Ca2+]i and [Na+]i changes. In new experiments, we used low-affinity, linear Na+ and Ca2+ indicators, laser fluorescence stimulation, and a sensitive camera-based detection system, combined with electrical stimulation and two-photon glutamate uncaging, to extend measurements of these spine parameters. We found that (1) almost all synaptically activated Na+ currents in CA1 hippocampal pyramidal neuron spines in slices from mice of either sex are through AMPA receptors with little Na+ entry through voltage-gated sodium channels (VGSCs) or NMDA receptor channels; (2) a spectrum of sodium transient decay times was observed, suggesting a spectrum of spine neck resistances, even on the same dendrite; (3) synaptically activated [Ca2+]i changes are very fast and are almost entirely because of Ca2+ entry through NMDA receptors at the time when the Mg2+ block is relieved by the fast AMPA-mediated EPSP; (4) the [Ca2+]i changes evoked by uncaging glutamate are slower than the changes evoked by synaptic release, suggesting that the relative contribution of Ca2+ entering through NMDA receptors at rest following uncaging is higher than following electrical stimulation.

Where have all the Orais gone? Commentary on “Orai1 channels are essential for amplification of glutamate-evoked Ca2+ signals in dendritic spines to regulate working and associative memory”

Orai1 channels were reported as critical contributors to the Ca2+ signal in hippocampal neurons underlying synaptic plasticity associated with learning and memory. We discuss the results in view of conflicting other reports that stressed the roles of Orai2 channels but failed to detect functions of Orai1 channels in these neurons.

Orai1 Channels Are Essential for Amplification of Glutamate-Evoked Ca2+ Signals in Dendritic Spines to Regulate Working and Associative Memory

SUMMARYStore-operated Orai1 calcium channels function as highly Ca2+-selective ion channels and are broadly expressed in many tissues including the central nervous system, but their contributions to cognitive processing are largely unknown. Here, we report that many measures of synaptic, cellular, and behavioral models of learning are markedly attenuated in mice lacking Orai1 in forebrain excitatory neurons. Results with focal glutamate uncaging in hippocampal neurons support an essential role of Orai1 channels in amplifying NMDA-receptor-induced dendritic Ca2+ transients that drive activity-dependent spine morphogenesis and long-term potentiation at Schaffer collateral-CA1 synapses. Consistent with these signaling roles, mice lacking Orai1 in pyramidal neurons (but not interneurons) exhibit striking deficits in working and associative memory tasks. These findings identify Orai1 channels as essential regulators of dendritic spine Ca2+ signaling, synaptic plasticity, and cognition.

Modulation of dendritic spines by protein phosphatase-1.

Protein phosphatase-1 (PP-1), a highly conserved multifunctional serine/threonine phosphatase, is enriched in dendritic spines where it plays a major role in modulating excitatory synaptic activity. In addition to established functions in spine maturation and development, multi-subunit holoenzyme forms of PP-1 modulate higher-order cognitive functions such learning and memory. Mechanisms involved in regulating PP-1 activity and localization in spines include interactions with neurabin and spinophilin, structurally related synaptic scaffolding proteins associated with the actin cytoskeleton. Since PP-1 is a critical element in synaptic development, signaling, and plasticity, alterations in PP-1 signaling in dendritic spines are implicated in various neurological and psychiatric disorders. The effects of PP-1 depend on its isoform-specific association with regulatory proteins and activation of downstream signaling pathways. Here we review the role of PP-1 and its binding proteins neurabin and spinophilin in both developing and established dendritic spines, as well as some of the disorders that result from its dysregulation.

MGluR2/3 mechanisms in primate dorsolateral prefrontal cortex: evidence for both presynaptic and postsynaptic actions

Cognitive deficits in psychiatric and age-related disorders generally involve dysfunction of the dorsolateral prefrontal cortex (dlPFC), but there are few treatments for these debilitating symptoms. Group II metabotropic glutamate receptors (mGluR2/3), which couple to Gi/Go, have been a focus of therapeutics based on rodent research, where mGluR2/3 have been shown to reduce axonal glutamate release and increase glial glutamate uptake. However, this strategy has had mixed results in patients, and understanding mGluR2/3 mechanisms in primates will help guide therapeutic interventions. The current study examined mGluR2/3 localization and actions in the primate dlPFC layer III circuits underlying working memory, where the persistent firing of ‘Delay cells’ is mediated by N-methyl-d-aspartate receptors and weakened by cAMP-PKA-potassium channel signaling in dendritic spines. Immunoelectron microscopy identified postsynaptic mGluR2/3 in the spines, in addition to the traditional presynaptic and astrocytic locations. In vivo iontophoretic application of the mGluR2/3 agonists (2R, 4R)-APDC or LY379268 onto dlPFC Delay cells produced an inverted-U effect on working memory representation, with enhanced neuronal firing following low doses of mGluR2/3 agonists. The enhancing effects were reversed by an mGluR2/3 antagonist or by activating cAMP signaling, consistent with mGluR2/3 inhibiting postsynaptic cAMP signaling in spines. Systemic administration of these agonists to monkeys performing a working memory task also produced an inverted-U dose–response, where low doses improved performance but higher doses, similar to clinical trials, had mixed effects. Our data suggest that low doses of mGluR2/3 stimulation may have therapeutic effects through unexpected postsynaptic actions in dlPFC, strengthening synaptic connections and improving cognitive function.

Polarization of the Endoplasmic Reticulum by ER-Septin Tethering

Polarization of the plasma membrane (PM) into domains is an important mechanism to compartmentalize cellular activities and to establish cell polarity. Polarization requires formation of diffusion barriers that prevent mixing of proteins between domains. Recent studies have uncovered that the endoplasmic reticulum (ER) of budding yeast and neurons is polarized by diffusion barriers, which in neurons controls glutamate signaling in dendritic spines. The molecular identity of these barriers is currently unknown. Here, we show that a direct interaction between the ER protein Scs2 and the septin Shs1 creates the ER diffusion barrier in yeast. Barrier formation requires Epo1, a novel ER-associated subunit of the polarisome that interacts with Scs2 and Shs1. ER-septin tethering polarizes the ER into separate mother and bud domains, one function of which is to position the spindle in the mother until M phase by confining the spindle capture protein Num1 to the mother ER.

CAMP-PKA phosphorylation of tau confers risk for degeneration in aging association cortex

The pattern of neurodegeneration in Alzheimer's disease (AD) is very distinctive: neurofibrillary tangles (NFTs) composed of hyperphosphorylated tau selectively affect pyramidal neurons of the aging association cortex that interconnect extensively through glutamate synapses on dendritic spines. In contrast, primary sensory cortices have few NFTs, even in late-stage disease. Understanding this selective vulnerability, and why advancing age is such a high risk factor for the degenerative process, may help to reveal disease etiology and provide targets for intervention. Our study has revealed age-related increase in cAMP-dependent protein kinase (PKA) phosphorylation of tau at serine 214 (pS214-tau) in monkey dorsolateral prefrontal association cortex (dlPFC), which specifically targets spine synapses and the Ca(2+)-storing spine apparatus. This increase is mirrored by loss of phosphodiesterase 4A from the spine apparatus, consistent with increase in cAMP-Ca(2+) signaling in aging spines. Phosphorylated tau was not detected in primary visual cortex, similar to the pattern observed in AD. We also report electron microscopic evidence of previously unidentified vesicular trafficking of phosphorylated tau in normal association cortex--in axons in young dlPFC vs. in spines in aged dlPFC--consistent with the transneuronal lesion spread reported in genetic rodent models. pS214-Tau was not observed in normal aged mice, suggesting that it arises with the evolutionary expansion of corticocortical connections in primates, crossing the threshold into NFTs and degeneration in humans. Thus, the cAMP-Ca(2+) signaling mechanisms, needed for flexibly modulating network strength in young association cortex, confer vulnerability to degeneration when dysregulated with advancing age.

Reactivation of the Same Synapses during Spontaneous Up States and Sensory Stimuli

In the mammalian brain, calcium signals in dendritic spines are involved in many neuronal functions, particularly in the induction of synaptic plasticity. Recent studies have identified sensory stimulation-evoked spine calcium signals in cortical neurons invivo. However, spine signaling during ongoing cortical activity in the absence of sensory input, which is essential for important functions like memory consolidation, is not well understood. Here, by using invivo two-photon imaging of auditory cortical neurons, we demonstrate that subthreshold, NMDA-receptor-dependent spine calcium signals are abundant during up states, but almost absent during down states. In each neuron, about 500 nonclustered spines, which are widely dispersed throughout the dendritic field, are on average active during an up state. The same subset of spines is reliably active during both sensory stimulation and up states. Thus, spontaneously recurring up states evoke in these spines "patterned" calcium activity that may control consolidation of synaptic strength following epochs of sensory stimulation.

Calcium Signaling in Dendritic Spines

Calcium (Ca(2+)) is a ubiquitous signaling molecule that accumulates in the cytoplasm in response to diverse classes of stimuli and, in turn, regulates many aspects of cell function. In neurons, Ca(2+) influx in response to action potentials or synaptic stimulation triggers neurotransmitter release, modulates ion channels, induces synaptic plasticity, and activates transcription. In this article, we discuss the factors that regulate Ca(2+) signaling in mammalian neurons with a particular focus on Ca(2+) signaling within dendritic spines. This includes consideration of the routes of entry and exit of Ca(2+), the cellular mechanisms that establish the temporal and spatial profile of Ca(2+) signaling, and the biophysical criteria that determine which downstream signals are activated when Ca(2+) accumulates in a spine. Furthermore, we also briefly discuss the technical advances that made possible the quantitative study of Ca(2+) signaling in dendritic spines.

Biphasic Synaptic Ca Influx Arising from Compartmentalized Electrical Signals in Dendritic Spines

Author SummaryThe vast majority of excitatory synapses in the mammalian central nervous system are made onto dendritic spines, small (< 1 fL) membranous structures stippled along the dendrite. The head of each spine is separated from its parent dendrite by a thin neck – a morphological feature that intuitively suggests it might function to limit the transmission of electrical and biochemical signals. Unfortunately, the extremely small size of spines has made direct measurements of their electrical properties difficult and, therefore, the functional implications of electrical compartmentalization have remained elusive. In this study, we use spatiotemporally controlled stimulation to generate calcium signals within the spine head and/or neighboring dendrite. By comparing these measurements we demonstrate that spines create specialized electrical signaling compartments, which has at least two functional consequences. First, synaptic stimulation, but not similar dendritic depolarization, can trigger the activation of voltage-gated calcium channels within the spine. Second, voltage changes in the spine head arising from compartmentalization shape the time course of synaptically evoked calcium influx such that it is biphasic. Thus, the electrical compartmentalization provided by spines allows for multiple modes of calcium signaling at excitatory synapses.

Functional Coupling between mGluR1 and Cav3.1 T-Type Calcium Channels Contributes to Parallel Fiber-Induced Fast Calcium Signaling within Purkinje Cell Dendritic Spines

T-type voltage-gated calcium channels are expressed in the dendrites of many neurons, although their functional interactions with postsynaptic receptors and contributions to synaptic signaling are not well understood. We combine electrophysiological and ultrafast two-photon calcium imaging to demonstrate that mGluR1 activation potentiates cerebellar Purkinje cell Ca(v)3.1 T-type currents via a G-protein- and tyrosine-phosphatase-dependent pathway. Immunohistochemical and electron microscopic investigations on wild-type and Ca(v)3.1 gene knock-out animals show that Ca(v)3.1 T-type channels are preferentially expressed in Purkinje cell dendritic spines and colocalize with mGluR1s. We further demonstrate that parallel fiber stimulation induces fast subthreshold calcium signaling in dendritic spines and that the synaptic Ca(v)3.1-mediated calcium transients are potentiated by mGluR1 selectively during bursts of excitatory parallel fiber inputs. Our data identify a new fast calcium signaling pathway in Purkinje cell dendritic spines triggered by short burst of parallel fiber inputs and mediated by T-type calcium channels and mGluR1s.

Membrane Potential Changes in Dendritic Spines during Action Potentials and Synaptic Input

Excitatory input onto many neurons in the brain occurs onto specialized projections called dendritic spines. Despite their potential importance in neuronal function, direct experimental evidence on electrical signaling in dendritic spines is lacking as their small size makes them inaccessible to standard electrophysiological techniques. Here, we investigate electrical signaling in dendritic spines using voltage-sensitive dye imaging in cortical pyramidal neurons during backpropagating action potentials and synaptic input. Backpropagating action potentials were found to fully invade dendritic spines without voltage loss. The voltage change in dendritic spines during synaptic input ranged from a few millivolts up to approximately 20 mV. During hyperpolarization of the membrane potential, the amplitude of the synaptic voltage in spines was increased, consistent with the expected change resulting from the increased driving force. This observation suggests that voltage-activated channels do not significantly boost the voltage response in dendritic spines during synaptic input. Finally, we used simulations of our experimental observations in morphologically realistic models to estimate spine neck resistance. These simulations indicated that spine neck resistance ranges up to approximately 500 Mohms. Spine neck resistances of this magnitude reduce somatic EPSPs by <15%, indicating that the spine neck is unlikely to act as a physical device to significantly modify synaptic strength.

Myosin Va Mutation in Rats Is an Animal Model for the Human Hereditary Neurological Disease, Griscelli Syndrome Type 1

A spontaneous neurological mutation, dilute-opisthotonus (dop), was discovered in our breeding colony of Wistar rats. We found that the mutation affected the gene encoding Myosin Va (MyoVA), an actin-based molecular motor. Analysis of the myosin Va (Myo5a) gene of the dop genome showed the presence of a complex rearrangement consisting of a 306-bp inversion associated with 217-bp and 17-bp deletions. A 141-bp exon is skipped in the dop transcript, producing a dop cDNA with a 141 in-frame deletion in the sequences encoding the head region. Expression of the MyoVA protein is severely impaired in the brains of dop homozygous rats, suggesting they have a null mutation for Myo5a. In a morphological analysis of the cerebella of dop rats, we found an absence of smooth endoplasmic reticulum (SER) and of inositol 1,4,5-triphosphate (IP3) receptors in the dendritic spines of Purkinje cells (PC). The SER acts as an intracellular Ca(2+) store and IP3-mediated Ca(2+) signaling in dendritic spines plays a critical role in synaptic regulation. We therefore measured synaptic transmission and long-term depression (LTD), a form of synaptic plasticity underlying cerebellar motor learning, at PC synapses in the cerebella of dop rats. We found that synaptic transmission at the PC synapses is largely normal, whereas the LTD is deficient due to a decrease in IP3-mediated Ca(2+) release from the SER in the PC spines of the dop cerebella. These findings may account for the ataxic movements and clonic convulsions displayed by dop rats. They also contribute to our understanding of the neurological disease mechanisms of the human hereditary disease Griscelli syndrome type 1, which is caused by mutation of the Myo5a gene.

Upstate Channel Switch

Medium spiny neurons (MSNs) of the striatum are key regulators of voluntary movement, and loss or deregulation of these neurons causes movement disorders, such as Huntington's or Parkinson's disease. These GABAergic neurons are activated by glutamatergic input to their dendritic spines. MSNs exist in a resting (—80 mV membrane potential) and an "upstate" (—50 mV membrane potential). Carter and Sabatini used 2-photon laser-scanning microscopy (2PLSM) and 2-photon laser uncaging of glutamate to investigate the calcium signals generated in resting or upstate MSNs in rat striatal slices. Calcium signals were larger and longer lasting in upstate cells, with the largest increase detected in the dendritic spine head. Using pharmacological inhibitors of different classes of voltage-gated calcium channels (VGCCs), the authors determined that stimulation of resting cells activates T-type and R-type VGCCs, and stimulation of upstate cells activates L-type and R-type VGCCs. Resting cells also respond to localized uncaging of glutamate with a fast Ca 2+ transient mediated by AMPA receptors and a slower, prolonged Ca 2+ transient mediated by N -methyl D aspartate (NMDA) receptors. Comparing responses in resting and upstate cells indicated a strong AMPA receptor contribution in resting cells and a dominant NMDA receptor contribution in upstate cells. These results indicate that differences in calcium signaling observed in resting and upstate MSNs arise from changes in the contributions of different classes of VGCCs and glutamate receptors. A. G. Carter, B. L. Sabatini, State-dependent calcium signaling in dendritic spines of striatal medium spiny neurons. Neuron 44 , 483-493 (2004). [Online Journal]

The Life Cycle of Ca 2+ Ions in Dendritic Spines

Spine Ca 2+ is critical for the induction of synaptic plasticity, but the factors that control Ca 2+ handling in dendritic spines under physiological conditions are largely unknown. We studied [Ca 2+] signaling in dendritic spines of CA1 pyramidal neurons and find that spines are specialized structures with low endogenous Ca 2+ buffer capacity that allows large and extremely rapid [Ca 2+] changes. Under physiological conditions, Ca 2+ diffusion across the spine neck is negligible, and the spine head functions as a separate compartment on long time scales, allowing localized Ca 2+ buildup during trains of synaptic stimuli. Furthermore, the kinetics of Ca 2+ sources governs the time course of [Ca 2+] signals and may explain the selective activation of long-term synaptic potentiation (LTP) and long-term depression (LTD) by NMDA-R-mediated synaptic Ca 2+.

Local Calcium Release in Dendritic Spines Required for Long-Term Synaptic Depression

We have used rats and mice with mutations in myosin-Va to evaluate the range and function of IP3-mediated Ca 2+ signaling in dendritic spines. In these mutants, the endoplasmic reticulum and its attendant IP3 receptors do not enter the postsynaptic spines of parallel fiber synapses on cerebellar Purkinje cells. Long-term synaptic depression (LTD) is absent at the parallel fiber synapses of the mutants, even though the structure and function of these synapses otherwise appear normal. This loss of LTD is associated with selective changes in IP3-mediated Ca 2+ signaling in spines and can be rescued by photolysis of a caged Ca 2+ compound. Our results reveal that IP3 must release Ca 2+ locally in the dendritic spines to produce LTD and indicate that one function of dendritic spines is to target IP3-mediated Ca 2+ release to the proper subcellular domain.

The morphoelectrotonic transform: a graphical approach to dendritic function

Electrotonic structure of dendrites plays a critical role in neuronal computation and plasticity. In this article we develop two novel measures of electrotonic structure that describe intraneuronal signaling in dendrites of arbitrary geometry. The log-attenuation Lij measures the efficacy, and the propagation delay Pij the speed, of signal transfer between any two points i and j. These measures are additive, in the sense that if j lies between i and k, the total distance Lik is just the sum of the partial distances: Lik = Lij + Ljk, and similarly Pik = Pij + Pjk. This property serves as the basis for the morphoelectrotonic transform (MET), a graphical mapping from morphological into electrotonic space. In a MET, either Pij or Lij replace anatomical distance as the fundamental unit and so provide direct functional measures of intraneuronal signaling. The analysis holds for arbitrary transient signals, even those generated by nonlinear conductance changes underlying both synaptic and action potentials. Depending on input location and the measure of interest, a single neuron admits many METs, each emphasizing different functional consequences of the dendritic electrotonic structure. Using a single layer 5 cortical pyramidal neuron, we illustrate a collection of METs that lead to a deeper understanding of the electrical behavior of its dendritic tree. We then compare this cortical cell to representative neurons from other brain regions (cortical layer 2/3 pyramidal, region CA1 hippocampal pyramidal, and cerebellar Purkinje). Finally, we apply the MET to electrical signaling in dendritic spines, and extend this analysis to calcium signaling within spines. Our results demonstrate that the MET provides a powerful tool for obtaining a rapid and intuitive grasp of the functional properties of dendritic trees.