2.1.

Slice Preparation, Solutions, and Electrophysiology

Experiments were approved by the Isere prefecture (Authorisation n. 38 12 01) and the specific protocol (n. 197) by the ethics committee of the Grenoble Institute of Neuroscience. Hippocampal slices ($250\mu \mathrm{m}$ thick) were prepared from 21 to 35 postnatal days old C57Bl6 mice as previously described¹¹ using either a VF-200 compresstome (Precisionary Instruments, Greenville, NC) or a Leica VT1200 (Leica, Wetzlar, Germany). Slices were cut in iced extracellular solution and incubated at 37°C for 1 h before use. The extracellular solution used contained (in mM) 125 NaCl, $26{\mathrm{NaHCO}}_3$, $1{\mathrm{MgSO}}_4$, 3 KCl, $1{\mathrm{NaH}}_2{\mathrm{PO}}_4$, $2{\mathrm{CaCl}}_2$, and 20 glucose, bubbled with 95% ${\mathrm{O}}_2$ and 5% ${\mathrm{CO}}_2$. The intracellular solution contained (in mM) $125{\mathrm{KMeSO}}_4$, 5 KCl, $8{\mathrm{MgSO}}_4$, $5{\mathrm{Na}}_2-\mathrm{ATP}$, 0.3 tris-GTP, 12 tris-phosphocreatine, and 20 HEPES, adjusted to pH 7.35 with KOH. To block ${\mathrm{Na}}^{+}$ and ${\mathrm{K}}^{+}$ channels in voltage clamp experiments, the external solution also contained $1\mu \mathrm{M}$ tetrodotoxin, 5 mM tetraethylammonium (TEA), 4 mM 4-aminopyridine, and 250 nM apamin, and the internal solution also contained 5 mM TEA. In this work, five ${\mathrm{Ca}}^{2+}$ indicators (all purchased from Invitrogen, Carlsbad, California) were used at the concentration of 1 mM: OGB1 (${\mathrm{K}}_{\mathrm{D}}=0.21\mu \mathrm{M}$, Ref. 12), OG6F (${\mathrm{K}}_{\mathrm{D}}=3\mu \mathrm{M}$, as reported by the vendor), OG5N (${\mathrm{K}}_{\mathrm{D}}=35\mu \mathrm{M}$, Ref. 13), BF2 (${\mathrm{K}}_{\mathrm{D}}=0.53\mu \mathrm{M}$, as reported by the vendor), and FuraFF (${\mathrm{K}}_{\mathrm{D}}=10\mu \mathrm{M}$, Ref. 14). ${\mathrm{Ca}}^{2+}$ indicators were dissolved directly into the internal solution. In voltage-imaging experiments, cells were loaded as previously described⁴ with the voltage-sensitive dye JPW1114 (Invitrogen). In calibrating experiments using the ${\mathrm{Ca}}^{2+}$-releasing caged compound nitrophenyl-EGTA (NP-EGTA)¹⁵ (Invitrogen), the internal solution also contained $150\mu \mathrm{M}$ ${\mathrm{CaCl}}_2$. All other chemicals were purchased either from Tocris (Bristol, UK) or Sigma-Aldrich (St. Louis, Missouri). Experiments were performed at 32 to 34°C using an Olympus BX51 microscope equipped with a $60\times /1.0\mathrm{NA}$ Nikon objective. Patch-clamp recordings were made using a Multiclamp amplifier 700A (Molecular Devices, Sunnyvale, California), and voltage and current signals were acquired with the analog-to-digital board of the CCD camera. The $V_m$ measured with the patch pipette was corrected for the junction potential ($-11\mathrm{mV}$) as calculated with the JPCalc software.¹⁶ In voltage clamp recordings, the ${\mathrm{Ca}}^{2+}$ current was evoked by depolarizing pulses from $-70$ to $-10\mathrm{mV}$ and measured in the soma by subtracting the scaled subthreshold current associated with a voltage step from $-70$ to $-60\mathrm{mV}$.

2.2.

Imaging System

A schematic of the imaging system is shown in Fig. 1(a). Simultaneous UV/blue light-emitting diode (LED) illumination from the epifluorescence port of the microscope was allowed by a 409 nm dichroic mirror (FF409, Semrock, Rochester, New York). UV light was either at 365 nm for photolysis or at 385 nm for excitation of Fura indicators fluorescence. The 365-nm LED was controlled by an OptoFlash (CAIRN Research Ltd., Faversham, UK) and the other LEDs were controlled by an OptoLED (Cairn). The image could be demagnified either by 0.5 or by 0.25, obtaining the fields of view shown in Fig. 1(b). The two images were separated by a 593 nm dichroic mirror and acquired with a dual-head NeuroCCD-SMQ camera (Redshirt, Decatur, Georgia) at $510\pm 42\mathrm{nm}$ (with the ${\mathrm{Ca}}^{2+}$ CCD) and at $>610\mathrm{nm}$ (with the $V_m$ CCD). The ${\mathrm{Ca}}^{2+}$ image was, therefore, the mirrored picture of the $V_m$ image. Whereas the camera has $80\times 80$ pixels per head (full resolution), to achieve the speed of 20 kHz, binned stripes of $26\times 4$ pixels were imaged. To achieve simultaneous illumination and detection of OG5N and JPW1114, both indicators were excited at 470 nm. The sensitivity of the VSD at 470 nm was about four times less than that at 532 nm. Thus, while an action potential is associated with a fractional change of fluorescence ($\mathrm{\Delta }F/F_0$) of 2 to 8% in the proximal apical dendrite at 532 nm, the same signal is associated with $\mathrm{\Delta }F/F_0$ of 0.5 to 2% at 470 nm. Using this configuration, the emission of JPW1114 detected by the ${\mathrm{Ca}}^{2+}$ CCD is negligible as shown in Fig. 1(c), and the emission of OG5N detected by the $V_m$ CCD is also negligible as shown in Fig. 1(d). Thus, it is possible to discriminate and quantify ${\mathrm{Ca}}^{2+}$ fluorescence from $V_m$ fluorescence.

Fig. 1

The imaging system. (a) Schematic of the imaging system including simultaneous UV/blue light-emitting diode illumination and the dual-head CCD camera (illustrated in the picture) for simultaneous $V_m$ and ${\mathrm{Ca}}^{2+}$ imaging; the image from the $60\times$ objective is demagnified by a coupler before detection. (b) Images of a micrometer slide from the two aligned heads of the camera using $0.5\times$ and $0.25\times$ demagnifing couplers; the distance between two adjacent lines is $10\mu \mathrm{m}$. (c) Top: fluorescence subimages of the apical dendrite of a CA1 hippocampal pyramidal neuron filled with 1 mM Oregon Green 488 BAPTA-5N (OG5N); resting fluorescence from the $V_m$ camera is $<5\%$ with respect to that from the ${\mathrm{Ca}}^{2+}$ camera; bottom: the fluorescence transient associated with an action potential is detected with the ${\mathrm{Ca}}^{2+}$ camera, and it is negligible at the $V_m$ camera. (d) Top: fluorescence subimages of the apical dendrite of another CA1 hippocampal pyramidal neuron filled with JPW1114; resting fluorescence from the ${\mathrm{Ca}}^{2+}$ camera is $<5\%$ with respect to that from the $V_m$ CCD; bottom: the fluorescence transient associated with an action potential is detected with the $V_m$ CCD, and it is negligible at the ${\mathrm{Ca}}^{2+}$ camera.

2.3.

Recording and Analysis of Ca²⁺ and V_m Optical Signals

${\mathrm{Ca}}^{2+}$ and $V_m$ recordings were performed at 20 kHz and data were initially expressed as $\mathrm{\Delta }F/F_0$. The high acquisition rate was necessary to prevent the loss of temporal information while applying the filtering procedure described below. ${\mathrm{Ca}}^{2+}$ recordings started 20 to 25 minutes after establishing the whole cell configuration, i.e., the time necessary to achieve the equilibrium of the indicator over the dendritic segment of recording. To improve the signal-to-noise ratio (S/N), fluorescence was generally averaged over 9 to 64 trials as specified in each figure legend and corrected for bleaching using trials without a signal. All data analysis was performed using software written in MATLAB® (The Mathworks, Natick, Massachusetts). The JPW1114-$\mathrm{\Delta }F/F_0$ signal was calibrated in terms of $V_m$ change using a previously demonstrated protocol based on wide-field photorelease of L-glutamate from the caged compound 4-methoxy-7-nitroindolinyl-caged-L-glutamate (MNI-glutamate).¹⁷ Briefly, a calibration of the JPW1114-$\mathrm{\Delta }F/F_0$ signal can be done if an electrical signal of known amplitude is available at all recording sites. In many neuronal types, activation of a large portion of ionotropic glutamate receptors makes them the dominant conductance and the resulting $V_m$ will be 0 mV in all the illuminated area. In CA1 hippocampal pyramidal neurons, a calibration is possible since the resting $V_m$ is uniform over the whole cell.¹⁸ Thus, the JPW1114-$\mathrm{\Delta }F/F_0$ signal associated with a saturating photorelease of L-glutamate will correspond to a change of $V_m$ from the resting $V_m$ to 0 mV. A representative cell where this procedure was applied is shown in Fig. 2(a). The JPW1114-$\mathrm{\Delta }F/F_0$ signal associated with an action potential was recorded from the initial $50\mu \mathrm{m}$ apical dendritic segment of a CA1 hippocampal pyramidal neuron [Fig. 2(b)]. After this recording, we added $1\mu \mathrm{M}$ tetrodotoxin to block voltage-gated ${\mathrm{Na}}^{+}$ channels and 1 mM MNI-glutamate to the external solution. Starting from the resting $V_m$ ($-60\mathrm{mV}$), we uncaged L-glutamate producing a depolarization to 0 mV. The glutamate-induced optical signal [Fig. 2(b), green] provided the calibration for the action potential. Statistical significance was evaluated using either the paired $t$ test or the two-population (2P) $t$ test.

Fig. 2

Calibration of JPW1114-$\mathrm{\Delta }F/F_0$ in terms of $\mathrm{\Delta }{V}_m$. (a) Initial apical dendritic segment of a CA1 hippocampal pyramidal neuron loaded with the VSD JPW1114; the region from where fluorescence was averaged is outlined in yellow. (b) JPW1114-$\mathrm{\Delta }F/F_0$ associated with an action potential or glutamate photorelease; the calibration protocol is applied from the resting membrane potential, which is assumed to be uniform over the cell; the massive ionotropic glutamate receptors activation drives the illuminated dendritic area to 0 mV. The action potential trace is from an average of 32 trials; the calibration trace was from an average of nine trials.

2.4.

Computer Simulations

The results of the analysis of the kinetics of the five ${\mathrm{Ca}}^{2+}$ indicators were compared with those obtained by computer simulations using a previously published theoretical framework.¹⁹ Briefly, we simulated the reaction of the dye ([D]) with ${\mathrm{Ca}}^{2+}$ in the presence of 1 mM of an endogenous buffer ([B]). For comparison with voltage clamp experiments, using the current measured with the patch electrode as ${\mathrm{Ca}}^{2+}$ current ($I_{\mathrm{Ca}}$), we numerically solved the set of differential equations:

The values of the association and equilibrium constants of the endogenous buffer were ${\mathrm{K}}_{\mathrm{ON}}^{\mathrm{B}}=2\times {10}^8{\mathrm{M}}^{-1}{\mathrm{s}}^{-1}$ and ${\mathrm{K}}_{\mathrm{D}}^{\mathrm{B}}={10}^{-5}\mathrm{M}$, while ${\mathrm{K}}_{\mathrm{OFF}}^{\mathrm{B}}={\mathrm{K}}_{\mathrm{ON}}^{\mathrm{B}}·{\mathrm{K}}_{\mathrm{D}}^{\mathrm{B}}$. The value of the association constant of all ${\mathrm{Ca}}^{2+}$ indicators was ${\mathrm{K}}_{\mathrm{ON}}^{\mathrm{D}}=6\times {10}^8{\mathrm{M}}^{-1}{\mathrm{s}}^{-1}$, as reported by Kao and Tsien,⁹ while ${\mathrm{K}}_{\mathrm{OFF}}^{\mathrm{D}}={\mathrm{K}}_{\mathrm{ON}}^{\mathrm{D}}·{\mathrm{K}}_{\mathrm{D}}^{\mathrm{D}}$ was derived for each different indicator from the ${\mathrm{K}}_{\mathrm{D}}$ values reported above. Numerical solutions were obtained using the MATLAB® function “ode45.”

3.1.

Comparative Analysis of the Kinetics of Different ${\mathrm{Ca}}^{2+}$ Indicators

The theoretical considerations described in the Introduction suggest that the kinetics of a fast ${\mathrm{Ca}}^{2+}$ current with a duration of a few milliseconds can be reconstructed from the fluorescence change of a low-affinity indicator. The ultimate strategy to test this hypothesis is to verify that the $\mathrm{\Delta }F/F_0$ ${\mathrm{Ca}}^{2+}$ signal is linear with the integral of the ${\mathrm{Ca}}^{2+}$ current measured, under voltage clamp, in the presence of ${\mathrm{Na}}^{+}$ and ${\mathrm{K}}^{+}$ blockers (see Materials and Methods). The protocol used in these tests, illustrated in Fig. 3(a), consisted of two depolarizing square pulses. The current associated with the first pulse, from $-70$ to $-60\mathrm{mV}$ not evoking a ${\mathrm{Ca}}^{2+}$ current, was scaled and subtracted from the current associated with a pulse from $-70$ to $+10\mathrm{mV}$. This procedure permitted the extraction of the ${\mathrm{Ca}}^{2+}$ current from the total current recording containing the leak current and the capacity transient. The integral of the ${\mathrm{Ca}}^{2+}$ current obtained in this way was then compared to the $\mathrm{\Delta }F/F_0$ signal. Figure 3(b) shows results from five representative cells, each recorded with a different indicator: the first 7 ms of $I_{\mathrm{Ca}}$ normalized to 1 (black traces), the corresponding normalized $I_{\mathrm{Ca}}$ integrals (red traces), and the associated normalized $\mathrm{\Delta }F/F_0$ signals (blue traces). The signals obtained in these experiments were faithfully mimicked by the results of computer simulations, reported on the right, performed as described in the Materials and Methods.

Fig. 3

Kinetics of different ${\mathrm{Ca}}^{2+}$ indicators investigated in voltage clamp. (a) Voltage clamp protocol consisting of two 16 ms voltage pulses from $-70\mathrm{mV}$, the first one below the threshold for activation of ${\mathrm{Ca}}^{2+}$ channels and the second one to $\sim 20\mathrm{mV}$; experiments were performed in the presence of ${\mathrm{Na}}^{+}$ and ${\mathrm{K}}^{+}$ channel blockers; the ${\mathrm{Ca}}^{2+}$ current ($I_{\mathrm{ca}}$) was extracted by subtraction of the scaled subthreshold current; the kinetics of the current were analyzed in correlation with that of the ${\mathrm{Ca}}^{2+}$ fluorescence change in the initial $60\mu \mathrm{m}$ segment of the apical dendrite; all data were averages of 16 trials. (b) $I_{\mathrm{ca}}$ and ${\mathrm{Ca}}^{2+}$ $\mathrm{\Delta }F/F_0$ from five representative cells filled with 1 mM of one of the following indicators: Oregon Green 488 BAPTA-1 (OGB1), Oregon Green 488 BAPTA-6F (OG6F), OG5N, Bis-Fura2 (BF2), or FuraFF; the integrals of $I_{\mathrm{Ca}}$ ($\int I_{\mathrm{Ca}}$) are also shown; signals are normalized to their maxima over the first 7 ms after the pulse beginning; simulations of the dye-${\mathrm{Ca}}^{2+}$ binding reaction are reported on the right. (c) From two of the representative cells filled either with OGB1 or with OG5N, the $\int I_{\mathrm{Ca}}$ and ${\mathrm{Ca}}^{2+}$ $\mathrm{\Delta }F/F_0$ normalized to their maxima over the first 4 ms after the pulse beginning; the difference between the two curves is also reported. (d) $\mathrm{Mean}\pm \mathrm{SD}$ of the surface of $\int I_{\mathrm{Ca}}-\mathrm{\Delta }F/F_0$ ($S$) obtained for each of the five indicators tested from the number of cells reported; OGB1: $0.185\pm 0.034$, $N=5$; OG6F: $0.049\pm 0.023$, $N=5$; OGB1: $0.007\pm 0.018$, $N=12$; BF2: $0.375\pm 0.150$, $N=4$; FuraFF: $0.002\pm 0.023$, $N=6$; the values of $S$ for OGB1 with respect to those for OG5N, and the values of $S$ for BF2 with respect to those for FuraFF were significantly different (two-population $t$ test, $*p<0.001$ and $**p<0.002$, respectively). Panels (a) and (c) were adapted from Ref. 10.

To quantify the difference of kinetics between the ${\mathrm{Ca}}^{2+}$ $\mathrm{\Delta }F/F_0$ signal and the $I_{\mathrm{Ca}}$ integral we computed the area ($S$) of the difference of the two curves normalized to 1 over the first 4 ms as shown in Fig. 3(c). The statistics of $S$ for the five groups of cells ($N=4$ to 12 for each indicator) is illustrated in Fig. 3(d). The values of $S$ with the two low-affinity indicators, OG5N and FuraFF, were statistically different from the values of $S$ with the high-affinity indicators, OGB1 and BF2 (2P $t$ test, $p<0.02$). In particular, the low-affinity indicators were able to track fast ${\mathrm{Ca}}^{2+}$ currents. OG5N-$\mathrm{\Delta }F/F_0$ has an S/N more than times three larger than that of FuraFF-$\mathrm{\Delta }F/F_0$ when associated with the same ${\mathrm{Ca}}^{2+}$ signal. For this reason, OG5N should be used for measuring relative small ${\mathrm{Ca}}^{2+}$ currents as those reported here. However, FuraFF can be better combined with JPW1114 for simultaneous $V_m$ and ${\mathrm{Ca}}^{2+}$ imaging⁷ and should be used for larger ${\mathrm{Ca}}^{2+}$ currents where fluorescence averaging over many trials is less critical. The tests presented here suggest that all organic ${\mathrm{Ca}}^{2+}$ indicators with ${\mathrm{K}}_{\mathrm{D}}$ for ${\mathrm{Ca}}^{2+}$ of $>10\mu \mathrm{M}$ can be potentially used to faithfully extract the time course of a fast ${\mathrm{Ca}}^{2+}$ current.

3.2.

Calibration of the OG5N-ΔF/F₀ Signal and Extraction of the Ca²⁺ Current

An important aspect of the ${\mathrm{Ca}}^{2+}$ imaging technique is its ability to provide an estimate of the intracellular ${\mathrm{Ca}}^{2+}$ concentration. In general terms, this estimate is not straightforward since the important information may involve knowing the free ${\mathrm{Ca}}^{2+}$ concentration (${[{\mathrm{Ca}}^{2+}]}_{\mathrm{FREE}}$) as well as the ${\mathrm{Ca}}^{2+}$ that binds to the dye and to the endogenous buffer. However, for a quantitative estimate of $I_{\mathrm{Ca}}$, the important information is exclusively the total ${\mathrm{Ca}}^{2+}$ concentration (${[{\mathrm{Ca}}^{2+}]}_{\mathrm{TOT}}$) entering the cell. The estimate of ${[{\mathrm{Ca}}^{2+}]}_{\mathrm{TOT}}$ corresponding to a particular $\mathrm{\Delta }F/F_0$ signal will allow determining the charge concentration and deriving the corresponding $I_{\mathrm{Ca}}$ volume density ($I_{\mathrm{Ca}},/V$).

A way to produce a ${[{\mathrm{Ca}}^{2+}]}_{\mathrm{TOT}}$ of known amplitude is to release ${\mathrm{Ca}}^{2+}$ from a caged compound. The cell in Fig. 4(a) was filled with an intracellular solution, also containing $300\mu \mathrm{M}$ of NP-EGTA and $150\mu \mathrm{M}$ ${\mathrm{CaCl}}_2$. NP-EGTA before photolysis is a high-affinity ${\mathrm{Ca}}^{2+}$ chelator (${\mathrm{K}}_{\mathrm{D}}=80\mathrm{nM}$). The ${\mathrm{K}}_{\mathrm{D}}$ decreases by a factor of 12,500 after photolysis.¹⁵ While in the pipette 50% of the NP-EGTA is bound to ${\mathrm{Ca}}^{2+}$, this percentage is unknown in the cell where it is regulated by the global ${\mathrm{Ca}}^{2+}$ homeostasis. However, when the cell of Fig. 4(a) was depolarized from $-70$ to $-10\mathrm{mV}$, a persistent OG5N-$\mathrm{\Delta }F/F_0$ signal $>20\%$ was observed. Since this signal typically corresponds to $>10$ times the signal associated with one action potential and ${[{\mathrm{Ca}}^{2+}]}_{\mathrm{FREE}}$ associated with an action potential in this dendrite type is $>100\mathrm{nM}$,²⁰ ${[{\mathrm{Ca}}^{2+}]}_{\mathrm{FREE}}$ at $-10\mathrm{mV}$ is $>1\mu \mathrm{M}$. Since ${\mathrm{K}}_D$ of NP-EGTA is 80 nM, at $V_m=-10\mathrm{mV}$, $>92\%$ of NP-EGTA is always bound to ${\mathrm{Ca}}^{2+}$. Under this condition, as shown in Fig. 4(a), the ${\mathrm{Ca}}^{2+}$ indicator is still not saturated since a further depolarization step of +50 mV produced an OG5N-$\mathrm{\Delta }F/F_0$ signal $>20\%$. Having established that at $V_m=-10\mathrm{mV}$, $\sim 300\mu \mathrm{M}$ is bound to NP-EGTA and available for release, the calibration protocol illustrated in Fig. 4(b) consisted of applying a sequence of 16 UV pulses (of 20 ms duration every 5 s) and measuring the OG5N-$\mathrm{\Delta }F/F_0$ signal associated with each pulse. The ${[{\mathrm{Ca}}^{2+}]}_{\mathrm{TOT}}$ released at the pulse $k$ follows the geometric progression:²¹

Fig. 4

Calibration of ${\mathrm{Ca}}^{2+}$ currents using ${\mathrm{Ca}}^{2+}$ photorelease. (a) OG5N-$\mathrm{\Delta }F/F_0$ from the initial $80\mu \mathrm{m}$ segment of the cell shown on the top (region of fluorescence average outlined) associated with a depolarization from $-70$ to $-10\mathrm{mV}$ (top) and from $-10$ to $+40\mathrm{mV}$ (bottom). (b) From the same cell filled with a solution containing $300\mu \mathrm{M}$ nitrophenyl-EGTA and $150\mu \mathrm{M}$ ${\mathrm{CaCl}}_2$, sequential UV-flashes (pulses) at $-10\mathrm{mV}$ produced an OG5N-$\mathrm{\Delta }F/F_0$ signal of decreasing amplitude (left); the OG5N-$\mathrm{\Delta }F/F_0$ amplitude versus the pulse was fitted with a geometric sequence to obtain the efficiency of each pulse ($\alpha =0.2$ in this example); considering the ${\mathrm{Ca}}^{2+}$ photoreleased by the first pulse, a signal of 1% corresponded to ${[{\mathrm{Ca}}^{2+}]}_{\mathrm{TOT}}=18\mu \mathrm{M}$ in this specific cell. (c) Calibrated OG5N-$\mathrm{\Delta }F/F_0$ (middle trace) associated with an action potential (top trace) and corresponding $I_{\mathrm{Ca}}/V$ (bottom trace). Data are from an average of 64 trials. Panel (a) was adapted from Ref. 10.

3.3.

Estimate of $I_{\mathrm{Ca}}/V$ Signals by ΔF/F₀ Filtering or Curve Fitting

The OG5N-$\mathrm{\Delta }F/F_0$ signal associated with an action potential can be measured from a $50\mu \mathrm{m}$ dendritic segment with good S/N, which can be further improved by averaging several trials. The extraction of $I_{\mathrm{Ca}}/V$, however, is based on the calculation of the time derivative, which requires the signal noise to be smaller than the signal change between two consecutive samples. A way to obtain this condition is to temporally filter the signal up to the limit of distortion of its kinetics. In our previous report, we have shown that the Savitzky-Golay algorithm is an optimal filtering tool for improving the S/N of the OG5N-$\mathrm{\Delta }F/F_0$ signal without significant temporal distortion using time windows of up to 20 to 30 samples.¹⁰ The application of this procedure allows extracting $I_{\mathrm{Ca}}/V$ from relatively large dendritic compartments and averaging several trials. The challenge for the improvement of data analysis was to go beyond the limitations of the filtering approach. This can be done by fitting the raw or the filtered OG5N-$\mathrm{\Delta }F/F_0$ signal with a model function obtaining a noiseless curve that mimics the time course of the OG5N-$\mathrm{\Delta }F/F_0$ signal. While the choice of the model might be arbitrary, a simple function that resembles the time course of the OG5N-$\mathrm{\Delta }F/F_0$ transient is the sigmoid. In particular, the OG5N-$\mathrm{\Delta }F/F_0$ signal normalized to its asymptotic value can be mimicked by the products of $N$ sigmoid functions $Y$:

Fig. 5

Extraction of the ${\mathrm{Ca}}^{2+}$ current using filtering or curve fitting. (a) Fluorescence images of a cell filled with OG5N; region A comprises $\sim 50\mu \mathrm{m}$ of dendrite from where fluorescence was averaged; region B is a single pixel. (b) Action potential signal from an average of 32 trials (left) or from a single trial (right). (c) From the same trials above, OG5N-$\mathrm{\Delta }F/F_0$ signals from the average of 32 trials in region A (left), from the average of 32 trials in region B (middle), or from the single trial in region B (right); the signals were either unfiltered (top, blue traces), filtered with the Savitzky-Golay algorithm at time windows of 10 (SG10), 20 (SG20), and 40 (SG40) samples, or fitted by the product of three sigmoid functions (FIT); the filter algorithm and the fit were implemented by the “smooth” and “lsqcurvefit” MATLAB® functions, respectively. (d) From the filtered or the fitted traces above, $I_{\mathrm{Ca}}/V$ were calculated for the three cases: average of 32 trials in region A (left), average of 32 trials in region B (middle), or single trial in region A (right); the approach of data fitting permits $I_{\mathrm{Ca}}/V$ extraction from sites of $\sim 2.4\mu \mathrm{m}$ using averaged trials or from larger regions in single trials.

3.4.

Simultaneous $V_m$ and $I_{\mathrm{Ca}}/V$ Optical Measurements

To illustrate the ability of simultaneous $V_m$ and $I_{\mathrm{Ca}}/V$ optical measurements to investigate ${\mathrm{Ca}}^{2+}$ currents and the behavior of underlying ${\mathrm{Ca}}^{2+}$ channels, we report here an analysis of the $I_{\mathrm{Ca}}/V$ associated with an action potential in the initial segment of the apical dendrite of the CA1 hippocampal pyramidal neuron. In the cell of Fig. 6(a), action potentials were evoked by current injection and recorded optically in the first $50\mu \mathrm{m}$ dendritic segment as reported in the top of Fig. 6(b). One action potential was evoked starting from $V_m=-60\mathrm{mV}$ and another action potential was evoked starting from $V_m=-80\mathrm{mV}$. The simultaneously recorded $I_{\mathrm{Ca}}/V$ signals are shown in the bottom of Fig. 6(b). The $I_{\mathrm{Ca}}/V$ associated with the action potential starting from $V_m=-80\mathrm{mV}$ was larger than that of the $I_{\mathrm{Ca}}/V$ associated with the action potential starting from $V_m=-60\mathrm{mV}$. The time course of $I_{\mathrm{Ca}}/V$ can be precisely correlated with the time course of $V_m$ as shown in Fig. 6(c). In 14 cells in which this protocol was applied, the mean $\pm \mathrm{S}.\mathrm{E}.\mathrm{M}.$ of the $I_{\mathrm{Ca}}/V$ peak in the first $50\mu \mathrm{m}$ dendritic segment was $7.2\pm 1.7\mathrm{pA}/{\mu \mathrm{m}}^3$ for the action potential starting at $V_m=-60\mathrm{mV}$ and $10.1\pm 1.4\mathrm{pA}/{\mu \mathrm{m}}^3$ for the action potential starting at $V_m=-80\mathrm{mV}$ as shown in Fig. 6(d). The $I_{\mathrm{Ca}}/V$ was consistently larger for the action potential starting at $V_m=-80\mathrm{mV}$ ($p<0.001$, paired $t$ test). As demonstrated in a previous report,¹⁰ the different $I_{\mathrm{Ca}}/V$ amplitude observed under the two $V_m$ conditions was mainly due to activation of T-type voltage-activated ${\mathrm{Ca}}^{2+}$ channels, which recovered from inactivation when the cell was hyperpolarized to $V_m=-80\mathrm{mV}$.²³

Fig. 6

Dendritic $I_{\mathrm{Ca}}/V$ associated with an action potential at different starting $V_m$. (a) Fluorescence images of a cell filled with OG5N and JPW1114; the region from where fluorescence was average is outlined. (b) Optical measurements of $V_m$ (top traces) and $I_{\mathrm{Ca}}/V$ (bottom traces) with an action potential starting either at $V_m=-60$ or $-80\mathrm{mV}$. (c) $I_{\mathrm{Ca}}/V$ superimposed to the optically recorded action potential in the two cases. (d) $\mathrm{Mean}\pm \mathrm{SEM}$ of the peak $I_{\mathrm{Ca}}/V$ associated with an action potential starting either at $V_m=-60$ or $-80\mathrm{mV}$ from 14 cells; the peak $I_{\mathrm{Ca}}/V$ was significantly higher for the action potential starting at $-80\mathrm{mV}$ ($p<0.001$, paired $t$ test).