Interpreting in vivo calcium signals from neuronal cell bodies, axons, and dendrites: a review

Abstract. Calcium imaging is emerging as a popular technique in neuroscience. A major reason is that intracellular calcium transients are reflections of electrical events in neurons. For example, calcium influx in the soma and axonal boutons accompanies spiking activity, whereas elevations in dendrites and dendritic spines are associated with synaptic inputs and local regenerative events. However, calcium transients have complex spatiotemporal dynamics, and since most optical methods visualize only one of the somatic, axonal, and dendritic compartments, a straightforward inference of the underlying electrical event is typically challenging. We highlight experiments that have directly calibrated in vivo calcium signals recorded using fluorescent indicators against electrophysiological events. We address commonly asked questions such as: Can calcium imaging be used to characterize neurons with high firing rates? Can the fluorescent signal report a decrease in spiking activity? What is the evidence that calcium transients in subcellular compartments correspond to distinct presynaptic axonal and postsynaptic dendritic events? By reviewing the empirical evidence and limitations, we suggest that, despite some caveats, calcium imaging is a versatile method to characterize a variety of neuronal events in vivo.


Introduction
Calcium imaging refers to optical methods for measuring the concentration of calcium ions in cells. In neuroscience, there has been an explosion in the number of studies that employ calcium imaging. For example, the method has been applied to awake animals to study, at the subcellular level, the role of dendritic calcium signals during perceptual performance; 1 at the singleneuron level, learning-related neural activity across the course of motor skill acquisition; 2 at the local-circuit level, dynamics of frontal cortical ensembles during decision-making; 3 and, at the network level, interactions between brain regions that underlie neurodevelopment. 4 Calcium imaging is also the primary method behind a recent large-scale effort to survey neural responses in the mouse visual cortex. 5 The rising popularity of calcium imaging is due in part to technical advances. The development of genetically encoded calcium indicators (GECIs)-fluorescent proteins that sense calcium and report via a change in emission amplitude or spectrum-enabled measurements with high signal-to-noise ratios. 6 Further work in protein engineering led to GECI variants with attractive properties such as a redshifted emission spectrum. 7 These GECIs can be introduced not only using viruses but are also available in a variety of transgenic animals. 8 Moreover, there are mature optical techniques for subcellular-resolution imaging in the intact brain based on two-photon-excited fluorescence. 9 New microscope designs additionally enable imaging deep in scattering tissues 10 and across a wide field of view. 11 Collectively, these advances have led to the widespread adoption of calcium imaging as a tool for neuroscience research.
A major reason for measuring calcium is that the influx of calcium ions is associated with electrical events, such as synaptic activation and dendritic spikes, that are difficult to measure with other methods. The inference is possible because we have accrued knowledge of the biophysical mechanisms that regulate the entry and life cycle of calcium ions in neuronal compartments. The inference is made stronger by computational models that describe calcium measurements in cellular compartments, which allows for a better dissociation between the desired goal to measure free calcium ions and the side effect of buffering by the calcium indicators. 12,13 These topics have been discussed extensively in other review articles that have focused on the utility of calcium imaging as a tool in neuroscience, [14][15][16] the mechanisms that regulate calcium in neurons, [17][18][19][20] the quantitative aspects of sensing calcium with fluorophores, [21][22][23] and procedures for analyzing calcium imaging data. 24 This article is intended to be a primer for interpreting calcium signals recorded from neurons with fluorescent indicators in vivo. Namely, if we see a fluorescent transient in the cell body, axon, or dendrite, what does the signal mean? Are the spatiotemporal dynamics consistent with a cellular event? Moreover, if the signal seems physiological, what can we say about the electrical event that gives rise to the calcium transient, and what in vivo calibration data would support the conclusion? Calibration is particularly relevant because in vivo neural dynamics are affected by background activity, neuromodulation, and GABAergic inputs, such that calcium signals could be markedly different in in vivo versus in vitro conditions. With these questions in mind, the main text is divided into sections based on various neural correlates commonly assigned to in vivo calcium signals. Within each section, we briefly introduce the biophysical basis, and then focus on experiments that have directly calibrated in vivo calcium signals against electrophysiological events. We highlight empirical details that are important for proper interpretation of calcium imaging data. We end each section by discussing limitations. We primarily use neocortical neurons as examples because many types of in vivo calibration data are available.
2 Somatic Calcium Signals: as a Proxy for Spiking Activity Somatic calcium signals have been used to infer spiking activity in neurons. By imaging an ensemble of neurons at singlecell resolution, one could delineate task-related neural activity during perceptual or cognitive behavior, 25 map the spatial organization of visually evoked neural responses, 26 and track modifications to neural activity across learning. 27 An action potential causes calcium influx in the neuronal cell body. For example, in layer 5 pyramidal neurons in the neocortex, calcium enters the soma through voltage-dependent calcium channels, including L-type channels that open in response to a large depolarization (∼20 mV), as well as N-, and P/Q-type channels. 28 The resting calcium concentration at the soma is ∼50 nM, and the increase due to a single action potential is estimated to be ∼40 nM. 29 This number may underestimate the actual amplitude, because even a moderate amount of fluorescent indicators would buffer and prolong the life cycle of calcium ions in a cell. 13,30 Measurements in the nearby proximal apical dendrite (30 to 50 μm from soma) suggest a rapid rise time (<2 ms to 90% of the peak amplitude; the measurement was limited by the kinetics of fluorescent indicators), and a decay time constant of ∼70 ms. 13 At the cell body, because of larger cytosolic volume, the decay time constant should be larger than the value at the proximal apical dendrite, and one study estimates a factor of ∼150%. 29 Therefore, although the action potential is a millisecond-scale event, the somatic calcium elevation has a duration that is longer by about two orders of magnitude.
Many studies have imaged calcium signals while recording spiking activity from the cell body in vivo to show a direct relationship between somatic calcium transients and action potentials. 6,[31][32][33] In one example, 6 putative excitatory somata were targeted for simultaneous two-photon calcium imaging using the fluorescent indicator GCaMP6s or GCaMP6f and juxtacellular recording in the neocortex of anesthetized mice [ Fig. 1(a)]. Fluorescence rose with each action potential [ Fig. 1(b)]. It should be emphasized that the signal reported by a fluorescent indicator is a convolution of the calcium transients and the indicator response. The choice of indicator matters, as evident by the different fluorescence profiles in response to a single spike for the two GECIs [ Fig. 1(c)]. In this case, GCaMP6s has slower single-spike kinetics (time to peak of 179 ms and decay time of 550 ms) compared to GCaMP6f (45 and 142 ms, respectively). 6 Furthermore, in the intervening periods between action potentials, the fluorescence was mostly unchanged [ Fig. 1(a)], suggesting that calcium elevations occurred only from suprathreshold depolarizations. This is consistent with the biophysical properties of the high-threshold calcium channels in the cell body. In practice, for cortical pyramidal neurons, it is possible to find a weak correlation between the subthreshold fluctuations in membrane potentials and the somatic calcium signals recorded in vivo. However, the source of that weak correlation probably does not come from the imaged cell, but rather originates from contamination of fluorescence signals from the surrounding neuropil, which would reflect the local network activity and correlate with membrane potentials of the imaged cell When action potentials are sparse relative to the imaging frame rate, a "kernel" can be estimated to describe the fluorescence response to a single action potential [ Fig. 1(c)]. Deconvolution of this kernel from the time-lapse fluorescent signal would yield spike times. 34,35 Having the kernel also enables other types of analyses. For example, spike-field coherence has been used to determine phase synchronization between neuronal firing and local oscillatory activity. 36 Analogously, from calcium imaging and field recordings, a fluorescence-field coherence could be determined. In one study that imaged spinal neurons while recording from motor nerves, the coherence allows for quantification of the locomotion phase during which the neurons contribute to motor pattern generation. 37 The kernel is required to account for the kinetics of the indicator to ensure the phase is accurate. In a few cases, such as granule cells in the Xenopus tadpole olfactory bulb 38 and principal neurons in the locust antennal lobe, 39 the somatic calcium signals do not strictly follow the spiking activity. This suggests that additional sources of calcium, such as low-threshold calcium channels or internal stores, are contributors and cannot be neglected for the soma of those cell types. These counterexamples highlight the need to calibrate for the cell type and animal model of interest.

Somatic Calcium Signals: for Neurons with High Firing Rates
Some neurons, such as the GABAergic fast-spiking cells in the neocortex, have high firing rates. Although spike inference becomes more difficult, calcium imaging may still be an attractive approach because some interneuron subtypes are few in numbers and sparsely distributed and, therefore, difficult to record with other methods. Applications of interneuron imaging include determining the orientation selectivity of GABAergic neuron subtypes in the rodent visual cortex 40 and dissecting functional responses of interneuron subtypes during delayed response tasks. 41 Several years ago, we performed simultaneous imaging and electrophysiological recording to provide evidence for a direct relationship between somatic calcium signals and firing rates in cortical GABAergic neurons 32 (Fig. 2). Certain interneurons, such as parvalbumin-expressing (PV) fast-spiking cells, have a high in vivo firing rate-up to an instantaneous rate of ∼35 Hz in anesthetized mice in our study and a mean rate of ∼50 Hz in awake, behaving mice. 42,43 For several reasons, as detailed at the end of this section, inferring the times of individual action potentials was imprecise in our original study. Nevertheless, most PV cells exhibited fluorescence signals that closely tracked the firing rate [ Fig. 2(a)]. Therefore, even in a case when individual spikes could not be resolved, calcium imaging may be used to read out changes in firing rate.
Perhaps the most notable insight from those experiments was the variability. There was variability across cells belonging to the same neuron subtype. For example, the 10 PV interneurons had substantial cell-to-cell variability in terms of fluorescence change per action potential [ Fig. 2(b)]. This may be due to differences in the concentration of calcium indicators, whether through uneven loading of synthetic dyes or differential expression levels of GECIs. There was also variability across the neuron subtypes. In particular, the fluorescence change per action potential was greatest for excitatory neurons, and ∼50% lower for somatostatin-expressing (SST) and PV interneurons [Figs. 2(c) and 2(d)]. These differences are probably due to endogenous calcium buffers in GABAergic interneurons. 44,45 Linearity in the spike-to-fluorescence relationship is important. Namely, one action potential should induce the same increase in fluorescence signal, regardless of the baseline calcium level. On average, with the synthetic dye OGB-1, the three cortical neuron subtypes exhibited fluorescence signals that scaled linearly with firing rates [ Fig. 2(d)]. For individual neurons, the majority of the PV cells had a linear response curve up to ∼30 Hz, although in a few selected cells, saturation was apparent at high firing rates [ Fig. 2(b)]. These observations are consistent with an independent in vivo calibration for PV interneurons. 46 A linear spike-to-fluorescence relationship depends on having a linear calcium-to-fluorescence relationship. Unlike OGB-1, GECIs that rely on cooperative calcium binding, such as GCaMP6, have nonlinear response curves. 23 If the saturation or nonlinear response profile is known, the distortion may be corrected to some extent in post hoc analysis. 47 Inferring individual spikes under the high firing rate condition is a challenging problem. Important factors include imaging speed, indicator kinetics, and signal-to-noise ratio. The need for high imaging speed is obvious, as the sampling rate must be faster than the frequency content of the underlying continuous signal to obey the sampling theorem. Indicator kinetics, including rise and decay times, are also crucial. When kinetics is slow relative to spike rate, fluorescence responses to adjacent spikes overlap and cannot be discerned. Signal-to-noise ratio-a factor of the indicator and experimental condition-must be sufficient to detect the fluorescence change due to a single spike. Optimization of these parameters and their interactions is a complex topic, as detailed in a prior study with numerical simulations, 47 and drives GECI engineering efforts. 23,48 4 Somatic Calcium Signals: for Measuring a Decrease in Firing Rate The somatic calcium transient due to an action potential has a near-instantaneous rise and then a relatively long decay. How much does the extended time course obscure the detection of a sudden decrease in firing rate? Figure 2(a) suggests that such decreases should be detectable. In that example, the PV interneuron has a high baseline activity in vivo, and fluorescence signals could track fluctuations above and below the median firing rate.
There are more explicit demonstrations that calcium signals can report a reduction in firing rate. In one experiment, a PV interneuron co-expresses an opsin for photoinhibition as well as a redshifted calcium sensor in vivo [ Fig. 3(a)]. The effect of photoinhibition was confirmed by the suppressed spiking activity recorded by a juxtacellular electrode. For a single trial involving a 5-s long silencing period, there was an obvious dip in the calcium signal when spikes were suppressed [red-shaded area, Fig. 3(a)].
A more thorough experimental demonstration of how calcium signals relate to reduced firing rate has been done in vitro in acute brain slices (see extended data Fig. 2 in Ref. 50). In particular, that study showed that a decrease in spike rate leads to a negative calcium transient, but hyperpolarization of the membrane potential without any action potential change had no effect on the calcium signal. This is expected because hyperpolarization should have minimal influence on the permeability of the calcium channels in the cell body. In other words, as a measure of inhibition, calcium cannot be used to detect inhibition in the form of hyperpolarization without spiking activity.
The same question can be answered with numerical simulations. For Fig. 3(b), we simulated how the somatic calcium signals would look if spike rate is halved for cells with varying amount of baseline firing. Notably, a reduction in calcium signal is obvious in single trials for neurons with high baseline activity, or by averaging across multiple trials for a wider range of firing rates. The more difficult cases are to discern a decrease in fluorescence if the neuron has low baseline firing, small reduction in spike rate, or only a few trials. However, this problem is not unique to calcium imaging, as peristimulus time histograms for spiking data is also noisy under these conditions [ Fig. 3(b)]. And as is the case for spike inference, the sensitivity of detecting a reduction in firing rate would also depend on indicator kinetics and signal-to-noise ratio.

Axonal Calcium Signals: as a Proxy for Presynaptic Activity
Calcium signals from axonal boutons reflect depolarization in the presynaptic terminals and therefore can provide information about the afferent activity. When applied to long-range projections, axonal calcium imaging has been used to study the flow of information from the primary visual cortex to higher visual areas, 51 determine the behavioral variables encoded by different afferent inputs to the motor cortex, 52 and map the spatial organization of long-range feedback projections. 53 Briefly, membrane depolarization at an axonal terminal leads to calcium influx. For example, in layer 2/3 pyramidal neurons, calcium entry near the presynaptic active zone is mediated by voltage-dependent calcium channels including P/Q-and Nsubtypes. 54,55 Calcium signals are larger at the synaptic terminals than the flanking axonal segments, presumably due to a nonuniform distribution of calcium channels. The presynaptic calcium influx for a single action potential was estimated to have a fast rise time of ∼1 ms and a decay time constant of ∼60 ms. An axonal calcium transient could be reliably elicited every time by an action potential, with an estimated mean increase of 500 nM at the terminal. Interestingly, when responses to a single action potential were measured across multiple axonal boutons from the same neuron, there was a more than 10-fold variation in the intensity of calcium transients. 56 This variability across boutons did not depend on distance from the soma but may instead depend on the postsynaptic cell type. 57 Calcium dynamics in the presynaptic terminals are also influenced by neuromodulators such as adenosine 55 and dopamine. 58 We have conducted experiments to assess the correlation between axonal calcium levels and afferent activation in an awake mouse 59 (Fig. 4). For these experiments, we targeted neurons in the retrosplenial cortex (RSC), which send dense axonal projections to the cingulate and secondary motor cortical regions (Cg1/M2). 60,61 An adeno-associated virus was used to express GCaMP6s in RSC neurons. We then imaged their axons in Cg1/M2 while simultaneously stimulated RSC using bipolar electrodes [ Fig. 4(a)]. In response to raising levels of electrical stimulation, there was a graded increase in the evoked fluorescence transients from axonal boutons [Figs. 4(b) and 4(c)]. The response profile to afferent activation is consistent with a previous in vitro calibration done in brain slices (see Supplementary Fig. 2 in Ref. 52). Altogether, these results provide evidence that the calcium signals recorded from axonal compartments in vivo is related to depolarization of the afferents.
Because prior study has suggested substantial variability in calcium responses across boutons from the same cell, attempts to use data from a single axonal bouton to infer the firing rate of the presynaptic cell would be prone to large errors. Furthermore, the dependences of the axonal calcium influx on the postsynaptic cell type and neuromodulators mean that an aggregate analysis including many boutons would bias toward subpopulations of terminals with larger calcium amplitudes. These are issues that will affect the interpretations until we gain a deeper understanding of the factors that influence calcium elevations in the axon.

Axonal Calcium Signals: as a Correlate of Neuromodulator Release
Axonal calcium signals may relate to neuromodulator release, particularly if calcium indicators are expressed in principal cells of a neuromodulatory system. For example, calcium signals can be imaged from cholinergic axons to investigate the role of acetylcholine during active behavior, 62,63 from cholinergic and noradrenergic axons to study pupil-related arousal, 64 and from dopaminergic axons to relate to locomotion and rewardbased behavior. 65 In these examples, neuromodulator release might not have been explicitly inferred, but nevertheless the calcium signals are often interpreted by comparing with previous studies that measure extracellular concentrations of the neuromodulators using methods such as microdialysis or fast-scan cyclic voltammetry. At least one study has empirically tested the relation between calcium signals and evoked neuromodulator release. 66 Stimulation of the medial forebrain bundle leads to the release of dopamine in the striatum. This is an ideal testbed because the evoked dopamine transient is large. In this study, a carbon-fiber microelectrode was inserted into the striatum for cyclic voltammetry measurements of extracellular dopamine concentration There are a number of caveats relating axonal calcium signals to neuromodulator release. Figure 5 shows that the calcium signals can track rapid phasic changes in dopamine concentration; however, the tonic level may not be detectable, as the calcium indicator can report relative changes but not the absolute amount of axonal activity. Furthermore, although an action potential would reliably depolarize the presynaptic terminal and cause calcium influx, the next steps in the chain of events involve the probabilistic release of a synaptic vesicle, and then the discharge and diffusion of several thousand neuromodulator molecules from a vesicle into extracellular space. As a result, the inference of neuromodulator levels from axonal calcium signals is complicated by additional, stochastic steps. Thus, although in vivo evidence suggests that the inference is reasonable when averaging across many axons and numerous trials, the correlation is likely much weaker at the single-axon level.

Dendritic Calcium Signals: as a Readout of Backpropagating Action Potentials
In dendrites, membrane depolarization can reflect a variety of passive and active electrical processes. 17,18 One important source of dendritic calcium elevations is the backpropagating action potential (bAP). A bAP occurs because an action potential initiated close to the soma can travel bidirectionally, such that it would not only continue along the axon but also propagate backward into the dendritic tree. As a retrograde signal of neuronal output to the dendritic tree, the bAP may play important roles in synaptic plasticity and associative learning. 67 Propagation of the bAP relies on active conductances including voltage-activated sodium channels. 68 In the absence of synaptic inputs, calcium can enter the dendritic shafts and spines through voltage-gated calcium channels. 54 The channel subtypes involved vary depending on the cell type. 17 The bAP is present in a variety of cell types, such as cortical pyramidal neurons, 68 cortical GABAergic bitufted interneurons, 69 and striatal medium spiny neurons, 70 but is much attenuated in other cell types, such as cerebellar Purkinje cells. 71 Experiments that combine imaging with electrophysiology have demonstrated dendritic calcium transients that are coincident with action potentials recorded in the soma. 72,73 The more ideal and causal test would be to elicit action potentials by injecting current into the soma. [74][75][76] In one study, 77 in an anesthetized mouse, a layer 2/3 neuron in the visual cortex was targeted for whole-cell recording while a two-photon microscope monitors fluorescent signals in the proximal dendritic segments [ Fig. 6(a)]. Action potentials were evoked by current injection into the cell body. Although the bAP is around a millisecond in duration, the fluorescent transient is prolonged due to the life cycle of calcium and indicator kinetics. The fluorescent signals were linearly associated with the number of action potentials [ Fig. 6(b)]. The bAP-associated calcium signal spread along the proximal dendrite with noticeable attenuation at the farthest imaged locations [ Fig. 6(c)].
The amount of bAP-associated calcium influx is dependent on a number of factors. One important factor is the distance from the initiation site of the action potential. In anesthetized animals, for layer 2/3 pyramidal neurons, the bAP attenuates and broadens as a function of distance from the soma, such that the calcium elevation becomes negligible beyond 200 to 250 μm. 74,75 For layer 5 pyramidal neurons, beyond the main bifurcation point of the apical tuft, calcium influx is absent or unreliable for single bAP. 76 Distance is the determining factor, because unlike the apical tuft, there is considerable correlation between somatic firing and calcium transients in the more proximal apical trunk and in the basal dendrites of these neurons. 73 Other factors include differences in the morphology of the dendritic tree 78 or the distribution of dendritic voltage-gated channels.

Dendritic Calcium Signals: as a Readout of Dendritic Regenerative Events
A regenerative event may be initiated at the dendrites in response to the temporally synchronous and spatially clustered activation of many synaptic inputs. The resulting broad dendritic spike is accompanied by large-amplitude calcium influx. Calcium entry may be mediated through N-methyl-D-aspartate (NMDA)-type glutamate receptors and voltage-gated calcium channels. Their relative contribution is thought to depend on the dendritic location. 79,80 For example, in layer 5 pyramidal neurons in vitro, calcium elevations from dendritic spikes could be confined to the activated branch in the most distal, fine tuft dendrites for NMDA spikes 79 or spread to ∼50 to 150 μm from the initiation site in the apical tuft near the main bifurcation point for calcium spikes. [81][82][83] Unlike sodium action potentials, the depolarization from calcium spikes can last hundreds of milliseconds.
Simultaneous calcium imaging and dendritic patch-clamp recording of layer 5 pyramidal neurons have provided evidence for compartmentalized calcium elevations that are regulated locally in dendrites in vivo. An early in vivo study showed that dendritic calcium events and somatic action potentials are not always coupled-namely, sometimes there is somatic burst spiking but no detectable change in dendritic calcium, whereas other times there is only one spike but a large dendritic calcium transient near the main bifurcation point of the apical dendrite. 76 In a more recent study, 84 it was shown that moderate dendritic voltage events in the apical trunk were not associated with any detectable calcium signals in the distal tuft dendrites in an anes- when a depolarizing current step was injected at the apical trunk, the coincident arrival of a spontaneous voltage event would induce a longer-lasting plateau depolarization, which was accompanied by a large-amplitude calcium transient in tuft dendrites [box 3 in Figs. 7(c) and 7(d)]. Critically, the current step alone was not sufficient to induce detectable calcium signals in the distal tuft. The interpretation for these data is that the dendritic calcium transients were due to occurrences of regenerative plateau potentials in the apical compartment, on the basis of the stimulation location. Intriguingly, this study presented relatively widespread dendritic calcium signals across multiple distal tuft branches, which differs from a couple of other accounts of transients that are typically more spatially restricted 73,85 or branchspecific. 86 One challenge is that without the knowledge of the calcium signals in the apical trunk, some of the putative branchspecific signals may in fact be more global plateau potentials that have not invaded all branches, and thus masquerade as compartmentalized calcium transients. A recent study estimated only about 15% of the calcium signals in distal tufts are independent from those in the apical trunk in layer 5 pyramidal neurons during awake behavior. 87 Pharmacological manipulations could provide additional clues as to the origin of these dendritic calcium signals in vivo. 85,88 Nevertheless, more work is needed to unequivocally attribute in vivo dendritic calcium transients to specific types of nonlinear regenerative events.

Dendritic Calcium Signals: as a Readout of Synaptic Input
Dendritic spines are protrusions on the dendritic shaft. Most dendritic spines are functional glutamatergic synapses that receive excitatory inputs. Upon depolarization from an excitatory input, calcium ions enter the spine compartment with minimal outflow to the dendritic shaft. 89,90 The localized signal is unlike the situation for bAP in which calcium invades both spines and the connecting shaft. 54 For pyramidal neurons, a large portion of the synaptically evoked calcium influx is probably driven by NMDA receptors, 54,91 with some contributions by voltage-gated calcium channels. 92,93 Because the localized calcium transient is a correlate of synaptic activation, spine imaging in vivo is a powerful method to characterize the organization of synaptic inputs, for example, to understand how inputs are integrated to give rise to feature selectivity in visual cortical neurons. 77,94 Because subthreshold synaptic activation-one that occurs in the absence of somatic action potentials or other regenerative events-induces only localized influx, any calcium transient detected in the shaft and spine at the same time is likely due to other mechanisms such as bAP or dendritic spikes. Therefore, a common practice is to isolate the local component by removing those fluorescent transients that co-occur in the shaft and spine in post hoc analysis using a subtraction procedure. 6,95,96 As an additional benefit, noises that cofluctuate in the shaft and spine, for example, from motion artifact, would be reduced by the subtraction procedure. How well does the procedure work? To answer this question, we have imaged spontaneous calcium transients in apposing bouton-spine pairs in awake mice. More specifically, we expressed GCaMP6s in RSC excitatory neurons and the redshifted calcium sensor jRGEOC1a in Cg1/M2 neurons [unpublished data; Fig. 8(a)]. In Cg1/M2, putative connected bouton-spine pairs could be identified based on proximity [ Fig. 8(b)]. We followed a typical subtraction procedure, by using linear regression to estimate the shaft-spine signal ratio, which allows us to scale the shaft signal and subtract its contribution from the spine signal [ Fig. 8(c)]. As expected for functional synapses, the subtraction-isolated, local fluorescent transients from the dendritic spine were highly correlated with signals from the axonal bouton [ Fig. 8(d)]. To quantify the relationship, we converted the fluorescence transients into calcium events using a peeling algorithm, 47 and then calculated the conditional probability of observing a presynaptic event given a postsynaptic event. In an example bouton-spine pair, we estimated ∼70% of the postsynaptic events imaged in the dendritic spine were coincident with synaptic input [Fig. 8(e)]. By contrast, the estimate fell to ∼30% when the subtraction procedure was not used, suggesting greater nonsynaptic contributions to the spine calcium signal. Isolation of the local component may be improved if the regression considers the distinct calcium diffusion and decay characteristics in the shaft and spine compartments. 87 One caveat of the aforementioned subtraction method is that, by definition, the procedure removes synaptic inputs that correlate with the occurrences of dendritic spikes and bAPs. Arguably those may include the strongest and clustered patterns of inputs that affect spiking activity and synaptic plasticity. To mitigate this issue, synaptic calcium signals may be imaged in the absence of spiking by hyperpolarizing the cell body or usingpharmacology. 77,97 This would prevent bAP, although dendritic regenerative events may still occur in the distal compartment due to the space-clamp problem. Another caveat is that calcium enters dendritic spines predominantly through NMDAR, so we would report only those synaptic activations that are sufficiently strong to relieve the magnesium block. Because of these challenges in detecting the strongest and weakest activations, synaptic calcium signals are expected to report a fraction of the synaptic inputs arriving at a dendritic spine and should be interpreted accordingly.

Putting It All Together
From the viewpoint of an experimenter, current imaging techniques provide a limited picture of the entire neuronal structure. We typically visualize either the somatic, axonal, or dendritic compartment, and therefore it has been convenient to categorize calcium signals based on the imaging location. However, this classification ignores the dynamic nature of the physiology. Instead, if we consider from the vantage point of a neuron, a sodium action potential initiated near the soma would induce calcium influx in the cell body, and then would propagate and elevate calcium also in the axon and proximal dendrite. Or take the case of synaptic inputs, which initially elevate calcium in spines, but together a strong barrage of inputs could lead to a regenerative event that is accompanied by more widespread dendritic calcium signals. 98,99 In a more complex situation, for example, in layer 5 pyramidal neurons, subthreshold synaptic inputs may pair with a bAP to drive plateau potentials and burst firing at the soma 100 -a sequence of events that is expected to induce calcium influx in almost all compartments of a neuron.
Presumably the more complex sequences of physiological events are more prevalent during active behavior. This is because the strength of regenerative events such as the bAP is boosted by synaptic inputs, which are more frequent and powerful in vivo and in awake conditions. 101,102 GABAergic neurons have complex firing patterns in vivo, and the strengthening or relief of inhibition could strongly influence calcium spikes 103 and control calcium influx into dendritic spines. 104 Indeed, dendritic calcium signals were found to be substantially enhanced in the same animal when awake rather than anesthetized. 105 Putting it all together, instead of considering calcium elevations from isolable events in various compartments, one can move toward using the overall spatiotemporal pattern of calcium signals across the entire cell to infer the underlying spatiotemporal dynamics of electrical depolarization in the neuron. . (e) The probability of detecting a presynaptic calcium event in the bouton within AE0.276 s (i.e., ± the duration of one image frame) given a postsynaptic calcium event in the apposing spine, either with subtraction or no subtraction of the shaft contribution. Calcium events were determined from fluorescence traces using a peeling algorithm. Shuffled level was calculated by randomly shuffling the calcium event times of the bouton, and averaged across 100 replicates. These are unpublished data from the Kwan lab.

Looking Ahead
We need methods that can uncover calcium signals over a broader spatial scale. Some techniques, such as fiber photometry, provide no optical sectioning. Because calcium signals could come from a mix of somatic, axonal, and dendritic sources, the neural correlates should be interpreted with caution. One improvement is to use genetic strategies to restrict expression to the soma 106 or axons, 107 such that calcium indicators reside in only a specific cellular compartment; however, experiments would still suffer from the same problems as discussed in the last section.
To increase the spatial extent of imaging, emerging technologies enable data acquisition across multiple axial planes or from a volume. In this review article, most of the examples were acquired with two-photon microscopes. Using a high numericalaperture objective, the lateral resolution of this method is ∼0.5 μm and axial resolution is ∼2 μm, 108 sufficient to visualize small compartments such as single dendritic spines. To maintain this spatial resolution but now over greater spatial extent, twophoton microscopes have incorporated design elements such as electrically tunable lens, 109 Bessel focus, 110 and remote focusing. 87 Studies using these new microscopes have demonstrated rapid imaging of multiple neuronal compartments, such as numerous dendritic tuft branch locations along with the apical dendritic trunk or the cell body.
As the ability to report calcium transients and infer electrical events depends on the properties of the fluorescent indicator, the choice of the indicator should be matched to the needs of the experiment. For the latest generation of GECIs, this is exactly the rationale behind the multiple variants of the indicators. 48,111 For example, the most sensitive variant is useful for the detection of single action potentials in the soma. By contrast, a variant with less sensitivity but brighter baseline fluorescence is desirable for dendritic imaging, because the higher basal signal is helpful for confirming the presence of a spine.
The indicator development, together with new imaging technologies, promises to deliver the full richness of calcium dynamics in neurons. This will help with addressing the current limitations of the calcium imaging technique and enable more accurate interpretations of the results.

Disclosures
The authors have declared that there is no conflict of interest.