## Abstract

The evidence for an important hypothesis that cortical spine morphology might participate in modifying synaptic efficacy that underlies plasticity and possibly learning and memory mechanisms is inconclusive. Both theory and experiments suggest that the transfer of excitatory postsynaptic potential signals from spines to parent dendrites depends on the spine neck morphology and resistance. Furthermore, modeling of signal transfer in the opposite direction predicts that synapses on spine heads are not electrically isolated from voltages in the parent dendrite. In sharp contrast to this theoretical prediction, one of a very few measurements of electrical signals from spines reported that slow hyperpolarizing membrane potential changes are attenuated considerably by the spine neck as they spread from dendrites to synapses on spine heads. This result challenges our understanding of the electrical behavior of spines at a fundamental level. To re-examine the specific question of the transfer of dendritic signals to synapses of spines, we took advantage of a high-sensitivity Vm-imaging technique and carried out optical measurements of electrical signals from 4 groups of spines with different neck length and simultaneously from parent dendrites. The results show that spine neck does not filter membrane potential signals as they spread from the dendrites into the spine heads.

## Introduction

The hypothesis that the morphology and the resulting electrical properties of cortical spines have a role in modifying synaptic efficacy that underlies plasticity and possibly learning and memory has recently received considerable attention because of its critical implications for brain function (e.g., Nuriya et al. 2006; Grunditz et al. 2008; Bloodgood et al. 2009; Palmer and Stuart 2009; Yuste 2010). The direct experimental evidence, however, in favor or against this hypothesis is incomplete and inconclusive, mostly for technical reasons; spines are small and not accessible to conventional methods of electrophysiology. Thus, attempts to investigate the electrical role of spines initially depended on numerical simulations using estimates of electrical parameters based on morphology and diffusional properties (Koch and Poggio 1983; Koch and Zador 1993; Svoboda et al. 1996). More recent studies employed optical recordings of [Ca2+]i concentration changes and imaging with membrane potential indicators (Araya et al. 2006; Grunditz et al. 2008; Bloodgood et al. 2009; Palmer and Stuart 2009; Holthoff et al. 2010). Currently, the electrical structure of spines can be described by 2 theoretical predictions of fundamental importance: (a) the excitatory postsynaptic potential (EPSP) signal amplitude in the parent dendrite either could be a sole function of the dendritic input resistance and independent of the spine neck resistance (Koch and Zador 1993; Svoboda et al. 1996), or could be a complex function of spine neck resistance (Koch and Zador 1993; Araya et al. 2006; Grunditz et al. 2008; Bloodgood et al. 2009; Hao and Oertner 2012) depending on the presently unknown range of possible EPSP amplitudes in the spine head; (b) synapses on spine heads are not electrically isolated from voltages in the parent dendrite under all plausible physiological conditions (Jack et al. 1975; Wickens 1988; Koch and Zador 1993; Palmer and Stuart 2009). These 2 elementary predictions have broad implications because they restrain the role of anatomical and electrical characteristics of dendritic spines in signal integration and synaptic plasticity.

Regarding the first theoretical prediction on the spread of EPSP signals from spines to dendrites, experimental evidence based on recording somatic responses to 2-photon glutamate uncaging on individual spines (Araya et al. 2006), on Ca2+ imaging from individual spines (Grunditz et al. 2008; Bloodgood et al. 2009; Hao and Oertner 2012), and on voltage-sensitive dye recording of EPSP signals from individual spines (Palmer and Stuart 2009) is inconclusive. An experimental test of the second theoretical prediction based on measurements of electrical events from spines using second harmonic generation (SHG) imaging reported that slow electrical signals were attenuated significantly by the spine neck as they propagated from dendrites to spines. The degree of attenuation was a function of spine neck length implying, in contrast to the theory, that spine neck axial resistance is one of the key parameters controlling the transfer of electrical signals from dendrites to synapses on spines (Araya et al. 2006). This result has important implications. First, the use of steady-state signals to calibrate optical recordings (Palmer and Stuart 2009; Holthoff et al. 2010) is invalidated if slow signals are attenuated as they spread into the spines. Second, if slow signals are attenuated, cable theory demands that fast bAP signals are attenuated at least as much, if not more, along the same electrical path (e.g., Rinzel and Rall 1974). Furthermore, significant attenuation of bAP signals does not fit with other results from voltage-sensitive dye recordings showing that bAPs have the same size and shape in dendrites and spines (Palmer and Stuart 2009; Holthoff et al. 2010).

The experimental data showing that spines are electrically isolated from dendrites call into question our understanding of electrical properties of spines at the elementary level. To re-examine this problem, we took advantage of a recently developed high-sensitivity Vm-imaging technique (Holthoff et al. 2010; Popovic et al. 2011) and carried out optical measurements of electrical signals from 4 groups of spines with different neck length. Our results, interpreted with a multicompartmental computational model, showed that the spine neck does not filter either slow hyperpolarizing signals or fast bAP signals, as predicted by theory.

## Materials and Methods

### Computational Modeling

The spine model, which was constructed and simulated with NEURON 7.2 (Carnevale and Hines 2006), represented the spine as a cylinder (head) attached to the distal end of another cylinder (neck) (equivalent circuit in Fig. 1C). Anatomical and biophysical properties were adjusted to explore the effects of these parameters on attenuation of voltage spreading from the dendritic shaft (proximal end of the spine neck) to the spine head. Resting potential was −66 mV unless otherwise noted, and numerical integration used NEURON's default implicit Euler method, with dt 0.025 ms.

Figure 1.

Spine model. (A) Schematic diagram of a spine attached to a dendrite; morphology and dimensions correspond to an actual spine; V(dend): membrane potential of the dendrite at the base of the spine; V(head): membrane potential of the spine head. (B) The simplest conceptual model (equivalent electrical circuit) of a spine attached to a dendrite; R(neck): axial resistance of the spine neck; R(head): transmembrane resistance of the spine head. (C) Multicompartmental model of a spine attached to a dendrite with all membrane resistances and distributed capacitance preserved. (D) Simulation results obtained with each of the 3 sets of biophysical parameters described in the text for spine neck length of 1 μm, given a 100 mV spike in the dendrite starting from a resting potential of −66 mV. Spine neck and head diameters were 0.2 and 1 μm, respectively. Traces from different simulations are superimposed; note that there is no discernible difference between V(dend) and V(head) in all cases.

Figure 1.

Spine model. (A) Schematic diagram of a spine attached to a dendrite; morphology and dimensions correspond to an actual spine; V(dend): membrane potential of the dendrite at the base of the spine; V(head): membrane potential of the spine head. (B) The simplest conceptual model (equivalent electrical circuit) of a spine attached to a dendrite; R(neck): axial resistance of the spine neck; R(head): transmembrane resistance of the spine head. (C) Multicompartmental model of a spine attached to a dendrite with all membrane resistances and distributed capacitance preserved. (D) Simulation results obtained with each of the 3 sets of biophysical parameters described in the text for spine neck length of 1 μm, given a 100 mV spike in the dendrite starting from a resting potential of −66 mV. Spine neck and head diameters were 0.2 and 1 μm, respectively. Traces from different simulations are superimposed; note that there is no discernible difference between V(dend) and V(head) in all cases.

In the basic model, the diameter × length of the head and neck were 1 × 1 µm and 0.2 × 1 µm, respectively. In all simulations, the spine head was treated as a single compartment, and the neck was discretized into 15 compartments of equal length (nseg = 15), which was more than sufficient for spatial accuracy given the range of anatomical and biophysical properties that was explored.

Three different sets of biophysical properties were tried: 1 passive and the other 2 active. The passive model was based on (Palmer and Stuart 2009) and its “control” parameters were cytoplasmic resistivity (Ra) 105 Ω cm, specific membrane capacitance (Cm) 1 µf/cm2, and membrane leak conductance (g_pas) 1/17 000 S/cm2. One of the active models was based on (Tsay and Yuste 2002) but omitted their sodium current; its “control” parameters were temperature 25°C, Ra 80 Ω cm, Cm 0.8 µF/cm2, gbar_kf 0.27 µS/cm2, gbar_ks 0.67 µS/cm2, and g_pas either 1/160 000 S/cm2 (which was probably a typographical error in the paper) or the more likely 1/16 000 S/cm2. The other active model was based on Stuart and Spruston (1998) and assumed channel densities that corresponded to the most distal dendrites in that model, that is, the largest channel densities, to maximize whatever attenuation might occur; its parameters were temperature 35°C, Ra 68 Ω cm, Cm 1.54 µf/cm2, gbar_q 0.02 S/cm2, and g_pas 1/5357 S/cm2.

Two different test signals were applied to the proximal end of the spine neck via a “perfect” voltage clamp (SEClamp with series resistance rs 1000 Ω): a depolarizing spike waveform from resting potential that was based on a cubic spline fit to an optically recorded spike waveform, and a 50 ms × 50 mV hyperpolarizing step from resting potential. The amplitudes of these signals were monitored in the spine neck and spine head.

Source code for these models will be made available from ModelDB https://senselab.med.yale.edu/modeldb/ (Hines et al. 2004).

### Slices, Patch-Clamp Recording, and Intracellular Application of Dyes

All surgical and experimental procedures were performed in accordance with National and Institutional Animal Welfare Guidelines. Experiments were carried out on somatosensory cortex slices from 18–30-day-old mice (Swiss Webster [CFW], Harlan Laboratories, Indianapolis). All measurements were carried out at 32–34°C. The mice were decapitated following deep sodium pentobarbital (50 mg/kg) anesthesia, the brain was quickly removed, and 300 μm thick coronal cortical slices were cut in ice-cold solution using a custom made rotary slicer with circular blade (Specialty Blades Inc., Staunton, VA). Slices were incubated at 37°C for ∼30 min and then maintained at room temperature (23–25°C). The standard extracellular solution used during recording contained (in mM): 125 NaCl, 25 NaHCO3, 20 glucose, 2.5 KCl, 1.25 NaH2PO4, 2 CaCl2, and 1 MgCl2, pH 7.4 when bubbled with a gas mixture (95% O2, 5% CO2). Slicing was done in modified extracellular solution (in mM): 110 choline-Cl, 25 NaHCO3, 20 glucose, 2.5 KCl, 1.25 NaH2PO4, 0.5 CaCl2, and 7 MgCl2. Somatic whole-cell recordings were made with 4–6 MΩ patch pipettes using a Multiclamp 700B amplifier (Axon Instruments Inc., Union City, CA). The pipette solution contained (in mM): 120 K-gluconate, 3 KCl, 7 NaCl, 4 Mg-ATP, 0.3 Na-GTP, 20 HEPES, and 14 Tris-phosphocreatin (pH 7.3, adjusted with KOH) and 0.8 mM of the voltage-sensitive dye JPW3028 (Zecevic and Antic 1995; synthesized and provided by L. M. Loew, University of Connecticut, Farmington, CT). The somatic whole-cell recording data were not corrected for liquid junction potential.

Individual layer 5 pyramidal neurons were selectively labeled with a membrane impermeant voltage-sensitive dye by allowing free diffusion of the probe from a somatic patch pipette in the whole-cell configuration. We used the most successful voltage probe for intracellular application, JPW3028, which is a doubly positively charged analog of the ANEP series of lipophilic styryl dyes that is still sufficiently water soluble to be used for microinjection. Its close analog JPW1114 (Zecevic 1996) characterized by the same voltage sensitivity is available from Invitrogen as D6923. Glass pipettes were first filled from the tip with dye-free solution by applying negative pressure for about 15 s and then back-filled with the solution containing of the indicator dye (0.8 mM). Intracellular staining was accomplished in 15–60 min, depending on access resistance. After a sufficient amount of the dye diffused into the cell body, as determined by measuring the resting fluorescence intensity from the soma, the patch-electrode with the dye was detached from the neuron by forming an outside-out patch. The staining level was determined empirically as a compromise that attains a high level of fluorescence without causing damage by prolonged dialysis from the patch pipette. After the dye diffusion was completed, the preparation was typically incubated for an additional 1.5–2 h at room temperature to allow the voltage-sensitive dye to spread into the dendritic arbor. To obtain electrical recordings from the soma, the cell body was repatched using an electrode filled with dye-free intracellular solution before making optical measurements. APs were evoked by brief transmembrane current pulses delivered via a recording electrode attached to the soma in whole-cell configuration. Steady state hyperpolarizing signals were evoked under voltage clamp.

### Optical Recording

We used a stationary upright microscope (AxioExaminer D1 with zoom tube (0.5–4×), Carl Zeiss Microscopy LLC) equipped with 3 camera ports. One camera port had a standard, high spatial resolution CCD camera for infrared DIC video-microscopy (CCD-300-RC, Dage-MTI, Michigan City, IN). The second camera port had a fast data acquisition camera with relatively low spatial resolution (80 × 80 pixels) but outstanding dynamic range (14 bits) and exceptionally low read noise (NeuroCCD-SM, RedShirtImaging LLC, Decatur, GA). The third camera port had a CCD camera with high spatial resolution (1392 × 1024 pixels; Pixelfly-qe, PCO Imaging, Kelheim, Germany) mounted on a spinning-disc confocal scanner (Yokogawa CSU-10; Solamere Tech., Salt Lake City, UT) used to collect z-stacks of confocal images for detailed morphological reconstruction of dendritic spines.

The brain slice was placed on the stage of the microscope and the fluorescent image of the stained neuron projected by a water immersion objective (63×/1.0 NA, Carl Zeiss) onto the fast data acquisition CCD positioned in the primary image plane. This objective was selected as a compromise between imaging area, spatial resolution, and signal-to-noise ratio (S/N). Optical recording of voltage-sensitive dye signals from individual spines and parent dendrites was carried out in the wide-field epifluorescence microscopy mode. The superior spatial resolution of confocal and 2-photon fluorescence microscopy techniques as well as SHG microscopy technique are difficult to utilize in Vm imaging from small structures as these methods cannot generate sufficient sensitivity in terms of the S/N mainly because of the high fractional shot noise related to small number of photons available for collection (Kuhn et al. 2004; Dombeck et al. 2005; Kerr and Denk 2008) (but see Acker et al. 2011). A frequency-doubled 450 mW diode-pumped Nd:YVO4 continuous wave laser emitting at 532 nm (MLL532, Changchun New Industries Optoelectronics Tech. Co., Ltd., Changchun, China) was the source of excitation light. The laser beam was directed to a light guide coupled to the microscope via a single-port epifluorescence condenser (TILL Photonics GmbH, Gräfelfing, Germany) designed to provide approximately uniform illumination of the object plane. The fractional noise of low-noise solid-state lasers (RMS < 0.5%) is below typical fractional shot-noise in fluorescence voltage-sensitive dye recordings (Iwasato et al. 2000; Matsukawa et al. 2003; Zhou et al. 2007; Canepari et al. 2010; Foust et al. 2010). The laser was used as a light source in place of a conventional Xenon arc-lamp to maximize the sensitivity of Vm imaging by: 1) using a monochromatic excitation light at the red wing of the absorption spectrum to maximize Vm sensitivity of the dye (Loew 1982; Kuhn et al. 2004; Holthoff et al. 2010) and 2) increasing the intensity of the excitation light beyond the level that can be achieved by an arc-lamp. The excitation light was reflected to the preparation by a dichroic mirror with the central wavelength of 560 nm, and the fluorescence light was passed through a 610 nm barrier filter (Schott RG610). The image of a stained neuron was projected by an objective onto a CCD chip via a variable zoom tube of the microscope. At zoom magnification of 1× the CCD frame (80 × 80 pixels) corresponded to approximately a 30 × 30 µm area in the object plane with each individual pixel receiving light from an area of ∼0.4 × 0.4 µm. Vm imaging was carried out at variable optical magnifications within a range of 1× to 2×. With the improved sensitivity of Vm imaging, relatively good S/Ns could be obtained in single-trial recordings from individual spines. Modest signal averaging (typically 4–9 and rarely up to 25 trials) was used to improve the S/N further.

The conclusions derived from our measurements are based on comparison of optical signals recorded from different locations. Such a comparison is valid only if the light intensity is linearly proportional to the membrane potential over the entire range of signal amplitudes. This has been demonstrated repeatedly in experiments where the same dye has been shown to track the full-size action potential exactly in several neuronal types (Zecevic 1996; Antic et al. 1999; Antic 2003, Djurisic et al. 2004; Palmer and Stuart 2006), a result that implies a strictly linear relationship between the dye signal and the membrane potential in the entire physiological range.

### Data Analysis

Membrane potential signals were recorded typically for 10 ms at a frame rate of 5 kHz using a partial readout mode (a strip of 24 × 80 pixels of an 80 × 80 pixels CCD chip). The analysis and display of data were carried out using the NeuroPlex program (RedShirtImaging) written in IDL (ITT Visual Information Solutions, Boulder, CO) and custom Visual Basic routines. Under low-light conditions, the background fluorescence becomes a significant determinant of ΔF/F signal size. Raw data were first corrected for this effect by subtracting the average background fluorescence intensity determined from an unstained area on the slice. Subsequently, the signal alignment software was used to correct for temporal jitter in AP initiation as well as for possible small movements of the preparation during averaging. In the temporal domain, AP signals were aligned by cross-correlation of the electrically recorded APs in each trial to the reference signal acquired at the start of averaging. In the spatial domain, camera images were aligned in 2 dimensions offline by image cross-correlation (e.g., Gonzalez and Woods 1992) to compensate for possible small lateral movements of the preparation. The correct focus of the image in the z-dimension was verified before each individual trial; small adjustments were often necessary. The spatially and temporally aligned signals were averaged, and slow changes in light intensity due to bleaching of the dye were corrected by dividing the data by an appropriate dual exponential function derived from the recording trials with no stimulation (Grinvald et al. 1982). Dual exponential fitting requires an algorithm for least-squares estimation of nonlinear parameters. We used the Levenberg–Marquardt algorithm (Marquardt 1963). Implementation in Visual Basic was taken from: http://digilander.libero.it/foxes/optimiz/Optimiz1.htm. The waveform of the AP signal was reconstructed from a set of data points using Cubic Spline Interpolation, a piecewise continuous curve passing through each data point (Mathews and Fink 2004).

### Pharmacological Effects and Photodynamic Damage Associated with the VSD Technique

A number of previous studies documented that loading neurons with the voltage-sensitive dye used here (JPW 3028) at concentrations that are appropriate for imaging does not have a detectable pharmacological effect on action potential and resting membrane properties. Although excitation of this dye does eventually cause phototoxic effects, this damage only becomes evident after multiple trials. Thus, it is possible to complete many recordings (>25) of action potentials prior to any evidence of phototoxic effects in both invertebrate (Antic and Zecevic 1995; Antic et al. 2000) and vertebrate neurons (Antic et al. 1999; Antic 2003; Djurisic et al. 2004, 2008; Palmer and Stuart 2006; Canepari et al. 2007, 2010; Foust et al. 2010; Holthoff et al. 2010). In the present study, we accepted for analysis only those trials in which there was no evidence for phototoxic damage, as indicated by the lack of a significant change in the rate of rise or fall or width of action potentials as recorded in the soma and imaged from processes (see also Canepari et al. 2007; Foust et al. 2010). We limited the laser illumination of the soma and proximal dendrites on most trials through position of the field stop diaphragm of the microscope, to prevent phototoxic damage resulting from the high levels of dye in these regions. Imaging AP signals was only performed for brief, 10 ms periods and ∼1 min was allowed between trials. We confirmed that this electrochromic dye does not significantly increase the membrane capacitance of the labeled neuron as evident from a number of control measurements showing that the waveform of the electrically recorded action potentials remains identical after intracellular application of the dye (e.g., Canepari et al. 2007). The physical basis for the lack of the capacitive load effect, which is characteristic for some fluorescence resonance energy transfer probes as well as some protein voltage sensors, is that the interaction of the electric field with electrochromic dyes, such as that used here, leads to a charge movement across only a very small fraction of the membrane field (the size of the chromophore; Blunck et al. 2005).

## Results

The experimental and theoretical focus of this article is on the spread of electrical signals from the dendrite into a dendritic spine. Specifically, given the amplitude and time course of membrane potential at a particular dendritic location, what will be the amplitude and time course of membrane potential in the head of a spine attached to the dendrite at that point? Figure 1A illustrates the experimental situation. The outlined spine morphology and dimensions, obtained by supraresolution fluorescence STED microscopy, correspond to an actual living spine as reported by Nägerl and Bonhoeffer (2010). We first describe theoretical predictions from a multicompartmental numerical simulation constructed with NEURON (Hines and Carnevale 1997) followed by a description of experimental measurements from dendritic spines and parent dendrites using a Vm-imaging technique (Holthoff et al. 2010).

## Modeling Predictions

Figure 1B shows the simplest conceptual model corresponding to a spine attached to a dendrite. Figure 1C is a multicompartmental model of a spine that preserves all of the membrane resistances and distributed capacitance. The spine neck was represented with 15 compartments of equal length each characterized by axial resistance as well as transmembrane resistance and capacitance. The spine head was a single isopotential compartment. The multicompartmental model was tested for the sensitivity of model behavior to different passive parameters with parameter values spanning the entire range of physiologically plausible values. Initial results showed that the effective capacitance of the spine neck and the spine head membrane had no detectable effect on model behavior due to the small membrane surface area, confirming the omission of those capacitances from the conceptual model. The conceptual model ignores membrane resistance of the spine neck because the membrane area of the neck is only 1/10 to 1/5 of the membrane area of the spine head, which is extremely small in itself.

The electrical circuit in Figure 1B is a simple voltage divider, which predicts how electrical signals are transferred from the parent dendrite to the synapse on the spine head. By Ohm's law and Kirchhoff's current law, when a potential gradient appears between locations V(dend) and V(head) in Figure 1, a current

(1)
$$I\hbox{} = \displaystyle{{V(\hbox{dend})} \over {(R(\hbox{neck}) + R(\hbox{head}))}}$$

will flow through axial spine neck resistance R(neck) and spine head membrane resistance R(head). Thus

(2)
$$V\hbox{(dend)} = I \times (R\hbox{(neck)} + R\hbox{(head)})\,\hbox{and}$$

(3)
$$V\hbox{(head)} = I \times R\hbox{(head)}$$

The attenuation of voltage from the dendrite to the spine head can be expressed as a ratio:

(4)
$$\displaystyle{{V\hbox{(dend)}} \over {V\hbox{(head)}}} = \hbox{1} + \left[ {\displaystyle{{R\hbox{(neck)}} \over {R\hbox{(head)}}}} \right]$$

If the membrane resistance of the spine head is much larger than the axial resistance of the cytoplasm in the spine neck [R(head) >> R(neck)], as should be expected from a large difference in the resistivity of lipid membrane and the cytoplasm, then

(5)
$$\displaystyle{{V(\hbox{dend})} \over {V(\hbox{head})}} \sim 1$$

In this case, there will be no significant attenuation and the voltage signals in the parent dendrite will reach the synapse on the spine head unaltered.

Table 1

Anatomical and biophysical parameters that determine effective membrane resistance of the spine head (R(head)) and axial resistance of the spince neck (R(neck))

Spine morphology  Head diameter/length (μm)  Neck diameter/length (μm)  R m (KΩ cm2 R i (Ω cm)  R(neck) (GΩ)  R(head) (GΩ)
1/1  0.2/1  16  100  0.034  540
1/1  0.1/4  5.3  300  1.5  170
Spine morphology  Head diameter/length (μm)  Neck diameter/length (μm)  R m (KΩ cm2 R i (Ω cm)  R(neck) (GΩ)  R(head) (GΩ)
1/1  0.2/1  16  100  0.034  540
1/1  0.1/4  5.3  300  1.5  170

## Experimental Measurements

Conclusions based on modeling and on theoretical predictions are prone to errors and have to be confirmed by experimental measurements. The experiments were designed to provide evidence for the fundamental question of whether the spine neck is capable of filtering slow and fast electrical signals as they propagate from the parent dendrite into the spine head. Testing possible filtering effects of the spine neck required recording membrane potential changes from parent dendrites and individual spine heads with necks of different length. If the spine neck length (and its resistance) has a significant role in filtering dendritic signals, this should become apparent from our measurements.

We monitored signals from spines with widely different neck lengths using a voltage-sensitive dye imaging technology that has submicrometer and submillisecond spatiotemporal resolution and a 50–100-fold improvement in recording sensitivity over previous approaches (Araya et al. 2006; Nuriya et al. 2006; Palmer and Stuart 2009). The striking improvement in sensitivity is based on using a laser as an excitation light source (in place of a conventional Xenon arc lamp) at a monochromatic wavelength that carries the best signal. In addition, the laser allowed us to increase the intensity of the excitation light to the upper limit set by the photodynamic damage. This increased the emitted fluorescence intensity and improved the S/N (see Methods section). Individual L5 pyramidal neurons were loaded with a voltage-sensitive dye and examined under wide-field epifluorescence to select spiny dendritic branches in the superficial layer of the slice (<30 µm deep) for recording. We recorded from spines on both basal dendrites and radial oblique apical dendrites at the average distance from the soma of 47 ± 3.5 µm (range 30–80 µm). Detailed spine anatomy was captured at the end of the experiment from stacks of confocal images obtained with 488 nm laser light excitation of the voltage-sensitive dye using the Yokogawa spinning disk confocal scanner. The correlation between relatively low-resolution epifluorescence image of individual spines obtained with voltage-imaging CCD and the high-resolution spine anatomy reconstructed from confocal images is shown in Figure 2. The 3-dimensional confocal images allowed quantification of spine neck length with spatial resolution better than 0.5 µm.

Figure 2.

Spatial resolution and spine dimensions. (A) Fluorescence image of a dendritic spine in recording position obtained with low-resolution CCD for voltage imaging. (B) Low-magnification fluorescence image of a dendrite with spines reconstructed from a z-stack of high-resolution confocal images. The white rectangle outlines the region shown in panels A and C. (C) Confocal image of the same spines at high magnification.

Figure 2.

Spatial resolution and spine dimensions. (A) Fluorescence image of a dendritic spine in recording position obtained with low-resolution CCD for voltage imaging. (B) Low-magnification fluorescence image of a dendrite with spines reconstructed from a z-stack of high-resolution confocal images. The white rectangle outlines the region shown in panels A and C. (C) Confocal image of the same spines at high magnification.

The primary concern in these measurements was the sensitivity of optical recording (in terms of the S/N) of membrane potential transients at the spatial scale of individual spines, miniscule structures ∼1 µm in diameter. Figure 3 illustrates that, in favorable experiments (well-stained spine close to the surface of the slice), bAP signals could be recorded from spine heads in single-trial measurements at a frame rate of 5 kHz with the unprecedented S/N of ∼10. In less favorable cases, similar S/N required averaging signals from 4 to 25 trials. Signal averaging was carried out within this range (1–25 trials) until S/N ratio of at least 6 was attained.

Figure 3.

Sensitivity and spatial resolution. (A) Voltage-sensitive dye fluorescence image of a mushroom spine with a long neck in recording position obtained with CCD for voltage imaging. Single-trial recordings of bAP-related signals from spine head (location 1) and from an analogous region without spine (location 2) are shown on the right. (B) Similar sensitivity and spatial resolution of recording bAP signals from a stubby spine head separated from the dendrite by a very short spine neck; temporal average of 4 trials.

Figure 3.

Sensitivity and spatial resolution. (A) Voltage-sensitive dye fluorescence image of a mushroom spine with a long neck in recording position obtained with CCD for voltage imaging. Single-trial recordings of bAP-related signals from spine head (location 1) and from an analogous region without spine (location 2) are shown on the right. (B) Similar sensitivity and spatial resolution of recording bAP signals from a stubby spine head separated from the dendrite by a very short spine neck; temporal average of 4 trials.

Another vital concern regarding accuracy of bAP recordings from spines and parent dendrites was the spatial resolution that can be achieved in wide-field epifluorescence microscopy mode as ultimately determined by the amount of light scattering in the brain tissue. We found that the effect of light scattering was very small and often not detectable in the superficial layer of the slice (<30 µm deep). A recording of the bAP signal from the head of a long (2.2 µm) neck mushroom spine is shown in Figure 3A together with a recording from an analogous location at the same distance from the dendrite which did not contain a spine. Because the recording from the location without the spine had no detectable signal, it is clear that the signal from the spine head was not contaminated significantly by scattered light from the parent dendrite. Figure 3B shows a similar test carried out for a stubby spine with a very short (<0.5 µm) spine neck in close proximity to a parent dendrite. In this case, the effect of light scattering from the parent dendrite is detectable but its contribution to the signal recorded from the spine head was sufficiently small to be neglected.

We next determined empirically the required temporal resolution (frame rate) of optical recording for accurate reconstruction of the analog signal (Fig. 4). We have shown previously that a frame rate of 10 kHz was adequate for accurate reconstruction of the fastest AP signals from axons of cortical pyramidal neurons (Foust et al. 2010; Popovic et al. 2011). Because AP signals have slower dynamics in the dendrites, we verified that lower sampling rate of 5 kHz (but not 1 or 2 kHz) is sufficient for the correct reconstruction of AP signals from spines. Further increase in the frame rate to 10 and 20 kHz (which results in an increase in the high-frequency shot noise) produced the same result. A sampling rate of 5 kHz was used in all subsequent measurements because lower sampling rate increases recording sensitivity. Additionally, we verified that the sampling rate of 5 kHz was adequate for recording bAP signals from both spines and dendrites because the waveforms of these signals were identical (Fig. 4).

Figure 4.

Temporal resolution. Recordings of bAP signals from a dendritic spine (shown in upper micrograph) using frame rates from 1 to 20 kHz. Recordings from spine head (red) and parent dendrite (blue) are shown. Frame rates lower than 5 kHz did not allow accurate reconstruction of the bAP signal. Superimposed signals from the spine head and from the dendrite (right traces) scaled to the same height were identical.

Figure 4.

Temporal resolution. Recordings of bAP signals from a dendritic spine (shown in upper micrograph) using frame rates from 1 to 20 kHz. Recordings from spine head (red) and parent dendrite (blue) are shown. Frame rates lower than 5 kHz did not allow accurate reconstruction of the bAP signal. Superimposed signals from the spine head and from the dendrite (right traces) scaled to the same height were identical.

To test the degree of electrical filtering of slow, prolonged transients in the spine neck, optical signals corresponding to a long-lasting hyperpolarizing pulse applied in voltage-clamp mode (60 mV; 50 ms as measured with the electrode in the soma) were recorded from the spine head and the parent dendrite, as illustrated in Figure 5. The signals were collected from a total of 81 spines (from 31 mice; 37 slices; 37 individual neurons) classified into 4 groups according to the neck length: Group 1: short neck spines (neck < 0.5 µm); Group 2: medium neck spines (0.5 µm < neck < 1.0 µm); Group 3: long neck spines (1.0 µm < neck < 2.0 µm); Group 4: very long neck spines (4 µm > neck > 2.0 µm). The results showed, in 100% of individual cases in all 4 groups of spines, that the fractional signal (ΔF/F) corresponding to a steady state hyperpolarizing pulse was smaller in amplitude in the dendrite compared with the spine head: (Group 1: spine 7.5 ± 0.4%; dendrite 4.9 ± 0.2% [n = 19]; Group 2: spine 7.0 ± 0.4%; dendrite 4.6 ± 0.3% [n = 24]; Group 3: spine 7.6 ± 0.3%; dendrite 4.5 ± 0.2% [n = 19]; Group 4: spine 7.0 ± 0.4%; dendrite 4.6 ± 0.2% [n = 19]). Individual values and the summary results are shown graphically in Figure 6. The consistent difference in the amplitude of the optical signal in dendrites and spines is in the opposite direction from the hypothetical cable filtering effect. This result can be readily explained, however, by the known difference in sensitivity of optical recording from different locations on a neuron caused by the difference in the surface-to-volume-ratio (e.g., Djurisic et al. 2004). The smaller surface-to-volume ratio in the dendrite tends to decrease the sensitivity of voltage imaging in terms of the fractional signal size (ΔF/F) because the light from the dye in the intracellular volume contributes to the resting fluorescence (F) but does not contribute to the signal (ΔF) related to voltage transients across the surface membrane (Djurisic et al. 2004; Canepari et al. 2010).

Figure 5.

Steady-state pulse signal amplitude in spine head and parent dendrite. A typical measurement of a voltage-sensitive dye signal (ΔF/F) from a spine head (red) and from the dendrite at the base of the spine (blue) as indicated in the upper fluorescent image of a spiny dendrite in recording position. Optical signals are related to a long lasting hyperpolarizing membrane potential transient generated under voltage-clamp from a somatic patch-electrode (bottom trace).

Figure 5.

Steady-state pulse signal amplitude in spine head and parent dendrite. A typical measurement of a voltage-sensitive dye signal (ΔF/F) from a spine head (red) and from the dendrite at the base of the spine (blue) as indicated in the upper fluorescent image of a spiny dendrite in recording position. Optical signals are related to a long lasting hyperpolarizing membrane potential transient generated under voltage-clamp from a somatic patch-electrode (bottom trace).

Figure 6.

Steady-state signal amplitude as a function of spine neck length. Scatterplot of the amplitude of optical signals recorded from the spine head and parent dendrite from 4 groups of spines with different neck length. Optical signals were related to a long-lasting hyperpolarizing membrane potential transient. Mean ± SD shown for individual groups (left) and for all spines (right).

Figure 6.

Steady-state signal amplitude as a function of spine neck length. Scatterplot of the amplitude of optical signals recorded from the spine head and parent dendrite from 4 groups of spines with different neck length. Optical signals were related to a long-lasting hyperpolarizing membrane potential transient. Mean ± SD shown for individual groups (left) and for all spines (right).

To establish whether spine neck length has an effect on electrical filtering of long-lasting hyperpolarizing signals, we compared the mean hyperpolarizing signals in the spine head in 4 groups of spines. The results indicated that the mean hyperpolarizing signal in the spine head had the same amplitude in all 4 groups of spines, independently of the spine neck length; pairwise comparison between groups showed no significant differences with P > 0.26. As expected, the same result was obtained from the comparison of the mean signal amplitudes measured in the dendrites in the 4 groups of spines; pairwise comparison between groups showed no significant differences (P > 0.23). This result is consistent with a conclusion that spine neck length (and its electrical resistance) has no influence on the amplitude of the steady-state hyperpolarizing signal in the spine head. The summary result from all measurements (Fig. 6; n = 81) indicated that the mean values for the signal amplitude in the spine head and in the dendrite were 7.2 ± 0.2% and 4.6 ± 0.1%, respectively. The average spine-to-dendrite signal amplitude ratio was 1.54 presumably reflecting a difference in recording sensitivity caused by the difference in the surface-to-volume ratio. Indeed, the theoretical signal amplitude ratio for signals from a sphere and a cylinder is 1.5. From these results, we conclude that the long-lasting hyperpolarizing pulse has the same amplitude in the dendrite and in the spine head. An important implication of this result is that the optical signal related to long-lasting hyperpolarizing pulse can be used reliably to normalize multiple site optical recordings of other dendritic signals.

In a subset of dendritic spines (n = 71) from the same 4 groups with different neck lengths, we were able to measure backpropagated action potential signals and determine whether the signal amplitude and the waveform in spine heads were modulated as a function of spine neck length and input resistance. In each measurement, we recorded an evoked bAP signal simultaneously from the spine head and the parent dendrite as shown in Figure 7. This measurement was followed by recording of a steady-state hyperpolarizing pulse from the exact same locations as described above. Finally, the data from bAP recordings were corrected for the difference in sensitivity by normalizing the bAP signals to the steady-state signal from spines and dendrites. A scatter plot in Figure 8 shows raw (ΔF/F) values for bAP signal amplitudes in the spine heads and in the parent dendrites together with the bAP signal amplitudes in the spine heads corrected for the difference in sensitivity of optical recording.

Figure 7.

Backpropagating AP signal amplitude normalized to long-lasting hyperpolarizing transient. (A) Confocal fluorescence image (upper) and low-resolution image (lower) of a spine in recording position. Recording regions: spine head, red; dendrite, blue. (B) Optical signals related to bAPs and hyperpolarizing calibration pulses recorded simultaneously from identical locations: spine head, red; parent dendrites, blue. Left traces: unprocessed signals. Right traces: bAP spine signal normalized to long-lasting hyperpolarizing transients.

Figure 7.

Backpropagating AP signal amplitude normalized to long-lasting hyperpolarizing transient. (A) Confocal fluorescence image (upper) and low-resolution image (lower) of a spine in recording position. Recording regions: spine head, red; dendrite, blue. (B) Optical signals related to bAPs and hyperpolarizing calibration pulses recorded simultaneously from identical locations: spine head, red; parent dendrites, blue. Left traces: unprocessed signals. Right traces: bAP spine signal normalized to long-lasting hyperpolarizing transients.

Figure 8.

Backpropagating AP signal amplitude as a function of spine neck length. Scatterplot of the amplitude of optical signals related to bAPs recorded from the spine head and parent dendrite from 4 groups of spines with different neck length. Raw values (left) and normalized spine signals (right) are shown (mean ± SD).

Figure 8.

Backpropagating AP signal amplitude as a function of spine neck length. Scatterplot of the amplitude of optical signals related to bAPs recorded from the spine head and parent dendrite from 4 groups of spines with different neck length. Raw values (left) and normalized spine signals (right) are shown (mean ± SD).

The correction procedure is in agreement with previous experimental (Stuart and Häusser 1994) and modeling (Palmer and Stuart 2009) results indicating that slow membrane potential signals attenuate very little over relatively long distances (>150 µm) in the dendritic tree. Thus, the slow hyperpolarizing membrane potential change imposed in our experiments under voltage clamp is expected to have the same amplitude at 2 locations separated by a dendritic cable of 0.5–4 µm in length. The clear result from these measurements was that the amplitude and the time course of the bAPs in the spine heads and in the parent dendrites were indistinguishable in all 4 groups of spines. The summary result (Fig. 9) shows that the ratio between the bAP amplitude in the spine head and in the parent dendrite was equal to 1 for all 4 groups of dendritic spines with very small variations that were not statistically significant. The same result was obtained for the time course of the bAP signals as characterized by the full-width-at-half-height of the spike signal (Fig. 9). These results are in full agreement with modeling predictions.

Figure 9.

Amplitude and waveform comparison of bAP signals in spines and dendrites. (A) Superimposed scaled bAP signals from spine heads (solid line) and dendrites (dashed line) on expanded time scale; representative measurements from 2 spines. (B) Spine head/dendrite ratios for bAP signal amplitude and time course (FWHH) recorded in 4 groups of spines with different neck length.

Figure 9.

Amplitude and waveform comparison of bAP signals in spines and dendrites. (A) Superimposed scaled bAP signals from spine heads (solid line) and dendrites (dashed line) on expanded time scale; representative measurements from 2 spines. (B) Spine head/dendrite ratios for bAP signal amplitude and time course (FWHH) recorded in 4 groups of spines with different neck length.

## Discussion

Our study asked the question of how well is the second theoretical prediction concerning spread of membrane potential signals from dendrites to synapses on spine heads supported by experimental evidence? In a series of experiments designed to provide direct information on electrical behavior of spines by monitoring SHG signals, recordings of electrical events from dendrites and spines indicated that slow hyperpolarizing electrical pulses were attenuated considerably (up to 50%) as they spread from parent dendrites across the spine neck (Araya et al. 2006). There was a positive correlation between the spine neck length, which varied from ∼0.3 to ∼1.3 µm, and the degree of attenuation of the steady-state hyperpolarizing signal by the spine neck. This result indicated that spine neck dimensions and, presumably, its axial resistance can modify the spread of dendritic membrane potential signals to synapses on spines. In contrast to this result, 2 subsequent studies using voltage-sensitive dye imaging (Palmer and Stuart 2009; Holthoff et al. 2010) indicated that the amplitude and the time course of the bAP signals were indistinguishable in the spine and the parent dendrite implying, in full agreement with the theory, that there was no filtering and no voltage loss across the spine neck when fast signals propagate from dendrites to spines. The conclusions of Palmer and Stuart (2009) and Holthoff et al. (2010), however, depend on an assumption that spines are not electrically isolated from parent dendrites for steady-state hyperpolarizing signals, which were, consequently, used to calibrate optical signals related to bAPs on an absolute voltage scale. The postulate that steady-state hyperpolarizing signals have the same amplitude in the spine head and the parent dendrite was not tested experimentally in those studies. Here, we carried out experiments to test this assumption by monitoring voltage signals from 4 groups of spines with a wide range of different spine neck lengths. No correlation was found between the spine neck length and membrane potential signal amplitude in the spine head.

The reasons for the difference in the results of our study and previously reported data based on SHG recordings (Araya et al. 2006) are not clear. A few possibilities, however, can be discussed. First, the scatterplot of SHG data (Fig. 5 of Araya et al. 2006) indicates a weak correlation, which might change with larger sample size. Second, there are 2 critical limitations to SHG measurements: (a) a proper calibration of SHG signals from multiple locations in terms of membrane potential (on an absolute scale, in mV) cannot be carried out on the basis of electrical measurement from any one site. This is evident from large and unexpected variations found in the amplitude of the SHG signal corresponding to a spike of constant size; the fractional SHG signals related to APs varied by a factor ∼4 (400%) in different measurements from the soma and by a factor of ∼7 (700%) in different measurements from individual spines (Fig. 4 in Nuriya et al. 2006). Clearly, optical signal was not selectively dependent on membrane potential but was strongly influenced by other factors. This limitation, if not compensated for by an independent calibration of optical signals in terms of membrane potential for each recording location, will render direct comparison of SHG signal amplitudes from dendrites and spines inaccurate; (b) SHG imaging was characterized by low sensitivity (signals corresponding to ∼100 mV AP were 10–20 times smaller than the noise in recordings; Nuriya et al. 2006) and, thus, necessitated very long hyperpolarizing pulses on the order of seconds and extensive temporal averaging which increases potential errors in characterizing individual measurements.

## Funding

This work was supported by National Institute of Health (NS068407 to D.Z. and NS11613 to N.T.C.), National Science Foundation (IOS-0817969 to D.Z.), and by the Kavli Institute for Neuroscience at Yale (to D.Z.).

## Notes

We are grateful to Leslie M. Loew (Center for Cell Analysis and Modeling, UConn Health Center, Farmington, CT 06030, USA) for providing dyes. Conflict of Interest: Dejan Zecevic declares that he is a co-owner of the RedShirtImaging LLC., a company that develops CCD imaging system for Physiology. All other authors report no conflicts of interest.

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