| HOME | HELP | FEEDBACK | SUBSCRIPTIONS | ARCHIVE | SEARCH | TABLE OF CONTENTS |
|
|
|
|||||||
|
|||||||||
| ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
INNOVATIVE METHODOLOGY
1Laboratory of Chemical Pharmacology, Graduate School of Pharmaceutical Sciences, The University of Tokyo; and 2Precursory Research for Embryonic Science and Technology, Japan Science and Technology Agency, Tokyo, Japan
Submitted 25 January 2008; accepted in final form 1 July 2008
 |
ABSTRACT |
|---|
|
|
|
INTRODUCTION |
|---|
|
; Kerr et al. 2005, 2007; Ohki et al. 2005, 2006; Sato et al. 2007; Sohya et al. 2007; Stosiek et al. 2003) as well as to in vitro brain preparations (Cossart et al. 2003; Crepel et al. 2007; Ikegaya et al. 2004; MacLean et al. 2005; Mao et al. 2001; Sasaki et al. 2006, 2007).
Despite the wide applicability of fMCI, there are still some technical problems. The spike reconstruction procedure, which is time consuming, inevitably includes artificial errors. To resolve this problem, several methods have been used to automatically reconstruct neuronal events from raw fluorescence signals. They include template-matching algorithms (Kerr et al. 2005), reverse correlation (Ramdya et al. 2006), threshold crossing of 
F/F and/or its derivative (Cossart et al. 2003; Ikegaya et al. 2004) and a novel detection algorithm for rodent cortex in vivo (Greenberg et al. 2008). In addition, calcium transient deconvolution (Yaksi and Friedrich 2006) and its relevant, more flexible algorithm (Moreaux and Laurent 2007) have been developed to estimate the firing rates from calcium fluctuations. These methods are simple and convenient but may sometimes be too sensitive to optical noises. Moreover the thresholds for defining neuronal events must be determined empirically (or arbitrarily). In the present study, we have devised a new computational framework that can reconstruct the spike timings more precisely without being affected by any subjective factor.
To this end, we first scrutinized the properties of action potential-evoked calcium transients in hippocampal slice cultures. Although the basic waveforms of calcium transients have been characterized in the soma (Canepari et al. 1999; Lips and Keller 1999; Smetters et al. 1999) and dendrites (Helmchen et al. 1996; Markram et al. 1995) of a neuron intracellularly loaded with fluorophore through a patch pipette, the properties of the calcium transients in acetoxymethylester (AM)-loaded neurons remain unknown. Here we addressed the following issues: 1) loading efficiency of Oregon green 488 BAPTA-1AM (OGB-1AM), one of the most widely used calcium indicators in fMCI, into cultured slice preparations; 2) the cellular calcium source in calcium transients; and 3) the relationship between calcium transient kinetics and the number and frequency of spikes at the generally used low frame rates of 10–50 Hz. Information on how individual calcium transients are linked to spikes is essential not only for establishing a spike detection algorithm but also for properly interpreting the fMCI data. Through these investigations, we sought to develop a spike detection algorithm by combining principal-component analysis (PCA) and support vector machine (SVM).
|
|
METHODS |
|---|
|
Hippocampal slice cultures were prepared from postnatal day 7 Wistar/ST rats (SLC, Shizuoka, Japan) as previously described (Koyama et al. 2007), according to National Institutes of Health guidelines for the care and safety of laboratory animals. Briefly, rat pups were chilled with ice and decapitated, and the brains were removed and horizontally cut into 300-µm-thick slices using a DTK-1500 vibratome (Dosaka, Kyoto, Japan) and were immersed in aerated, ice-cold Gey's balanced salt solution (Invitrogen, Garthersburg, MD) supplemented with 25 mM glucose. Entorhino-hippocampal stumps were cultivated on Omnipore membrane filters (JHWP02500; Millipore, Bedford, MA) that were laid on plastic ring disks. The cultures were fed with 1 ml of 50% minimal essential medium, 25% Hanks' balanced salt solution (Invitrogen), 25% horse serum (Cell Culture Laboratory, Cleveland, OH), and antibiotics in a humidified incubator at 37°C in 5% CO2. The medium was changed every 3.5 days.
Functional multineuron calcium imaging
On days 7–14 in vitro, the slices were washed three times with oxygenated artificial cerebrospinal fluid (ACSF) consisting of (in mM) 127 NaCl, 26 NaHCO3, 3.3 KCl, 1.24 KH2PO4, 1.0 MgSO4, 1.0 CaCl2, and 10 glucose. They were transferred into a dish (35 mm diam) containing 2 ml of the dye solution and were incubated for 1 h in a humidified incubator at 37°C under 5% CO2 (Ikegaya et al. 2005; Morita et al. 2003; Takahashi et al. 2007). The dye solution was ACSF containing 10 µl of 0.1% OGB-1AM/DMSO (Invitrogen), 2 µl of 10% Pluronic F-127/DMSO (Invitrogen), and 2 µl of 5% Cremophor EL/DMSO (Sigma, St. Louis, MO). After being washed, the slices were incubated at room temperature for >30 min and were mounted in a recording chamber perfused with ACSF at 32°C. The fluorophores were excited at 488 nm using an argon-krypton laser (5–10 mW, 641-YB-A01; Melles Griot, Carlsbad, CA) and were visualized using a 507-nm long-pass emission filter. Images (653 x 492 pixels = 383 x 289 µm; 512 x 512 pixels = 520 x 520 µm: 14–16 bit intensity) were captured at 10–50 frame/s using a Nipkow disk confocal microscope (CSU10/CSU-X1; Yokogawa Electric, Tokyo, Japan), cooled CCD cameras (Cascade; Roper Scientific, Tucson, AZ; iXON DV887; Andor, Belfast, Northern Ireland, UK), upright microscopes (ECLIPSE FN1; Nikon, Tokyo, Japan; AxioSkop2; Zeiss, Oberkochen, Germany) equipped with water-immersion objectives (x20, 0.5 numerical aperture (NA); x40, 0.8 NA, Achroplan, Zeiss; x16, 0.8 NA, CFI75LWD16XW, Nikon), and Metamorph software (Molecular Devices, Union City, CA). Fast Z-dimension scanning along the optical axis was performed with a piezo actuator (Physik Instrumente) and its control unit (PCU100, Andor). Image compensation was not done.
The cell bodies of neurons were identified by eye to put the regions of interest (10-µm-radius circles) in which the average fluorescence was measured. For each cell, the change in somatic fluorescence (F/F) was calculated as (F1 –F0)/F0, where F1 is the fluorescence intensity at any time point, and F0 is the average baseline fluorescence intensity before and after the 10-s recording epoch. This normalization with a 20-s epoch around the target frame is needed to compensate photobleaching.
Two-photon imaging
Images of cells stained by the dyes were visualized using a two-photon laser scanning system based on a mode-locked Ti:sapphire laser with a 100-fs pulse width, 80-MHz pulse frequency, and 920-nm wavelength (Maitai; Spectra Physics, Mountain View, CA) and mounted on an upright microscope (BX61WI; Olympus). The excitation light was focused using a water-immersion objective (x20, 0.95 NA, XLUMPlanFI/IR; Olympus). The emitted fluorescence was detected using photomultiplier tube detectors (PMTs; Direct Detection System; Olympus).
Electrophysiological recording
Patch-clamp recordings from CA3 pyramidal cells were carried out using an Axopatch 700B amplifier (Molecular Devices, Union City, CA). For loose cell-attached and whole cell recordings, borosilicate glass pipettes (4–9 M
) were filled, respectively, with ACSF and an internal solution consisting of (in mM) 120 K gluconate, 20 KCl, 10 HEPES, 0.4 Na2-GTP, and 4 Mg-ATP and 50 nM CaCl2 (pH 7.2). OGB-1 potassium salt (Invitrogen) was dissolved in the intracellular solutions to attain a final concentration ranging from 1 to 200 µM. Signals were low-pass filtered at 1–2 kHz, digitized at 10 kHz, and analyzed using pCLAMP 9.2 software (Molecular Devices). All solutions were stored at –20°C, diluted immediately before use, and bath applied. The excitatory or inhibitory postsynaptic events were automatically extracted based on a single criterion, namely, a current size >5 pA.
Nissl staining
After recording, the slice cultures were immersed in a mixture of 4% paraformaldehyde, 1% Triton X-100, and red or green Neuro-Trace fluorescent Nissl (1:100; Invitrogen) in 0.1 M phosphate-buffered saline (PBS) for 1 h at room temperature.
Manual spike reconstruction
The spike times were manually reconstructed from the onset of the calcium transients using a custom-made software in Microsoft Visual Basic (Ikegaya et al. 2004).
Automatic spike reconstruction
Our automatic algorithm is composed of two steps, i.e., conditioning (learning) phase and test (spike detection) phase. In the conditioning phase, the parameters are tuned to give the most appropriate rate of spike detection from sample datasets. In the test phase, the algorithm with the best tuned parameters extracts spike signals from datasets different from those used in the conditioning phase. The data used for conditioning was collected from 10 cells. The average recording period was 312 ± 137 s (same as in Figs. 4 and 5; 1,782 spike signals and 2,000 nonspike signals). All routines were written in Matlab (The Math Works).
|
|
(see Fig. 5A, top). Note that ts and te represent negative and positive values, respectively. Thus the vector length N was equal to 1 + (te – ts)/f, where f denotes the interframe interval (here, f = 100 ms). Then each sample vector was normalized such that all components of the vector were between 1 and 0. These components reflect the characteristic shape of the calcium transient with a sharp rise followed by a slow decay.
Next, one dimension was added in the vector, as follows
 |
Using PCA, two principal dimensions were extracted from the set of vectors. To evaluate the degree of separation of the two distributions (with or without spikes) on the principle component (PC) coordinate (see Fig. 5B), we used Jensen-Shannon (JS) divergence, which quantifies the degree of dissimilarity between the two distributions. The coordinate system spanned by the first two PC components was divided into 50 x 50 grids in each of which the distribution probability of data points was calculated. The distributions of vectors with and without spikes were defined as p and q, respectively.
If the two probability distributions are given by p and q, respectively, JS is calculated in the following manner
 |
 |
The JS divergence assumes a value between 0 and log 2 with higher values indicating better separation. Unlike the Kullback-Leiber divergence, the JS divergence is symmetric between p and q.
Next, in the two PC coordinates, linear SVM was applied to determine the discriminant border between the two regions (Smola and Schölkopf 2004). The SVM-code is available at http://www.kyb.tuebingen.mpg.de/bs/people/chapelle/primal/. We defined the SVM score as the relative distance from each data point to the separating line as follows
 |
We repeatedly conditioned the SVM by modulating the vector w that is perpendicular to the best separating line and the intercept b in order that the SVM score assumes a positive value if the vector x contains spikes. Through the conditioning (or training) process, we obtained the most optimal parameters w and b with the following test phase.
TEST PHASE.
From a time series of the fluorescent calcium trace F(t), the windows that contain N data points around the focused time T (in ms) were successively slid along the time axis of the parent dataset and each was defined as a vector 
as follows
 |
Similar to the conditioning phase, each vector component was normalized such that the maximum and minimum component values assumed 1 and 0, respectively. Further, one component was added to the vector as follows.
 |
The vector was decomposed into two dimensions by PCA using the same eigenvectors as those used in the conditioning phase, and the SVM score was calculated using w and b.
At the points where the SVM scores assumed local maxima >0, the vectors were defined as spike signals.
Statistics
We reported the data as the means ± SD. The signal-to-noise (SN) ratio was defined as the amplitude of spike signals divided by the SD of fluorescence intensity in the trace, ANOVA Student's t-test, and Tukey's test were performed to assess the significance of the differences. P values <0.05 were considered statistically significant.
|
|
RESULTS |
|---|
|
Hippocampal slice cultures were incubated in OGB-1AM solution, a membrane-permeable precursor of the membrane-impermeable calcium indicator OGB-1. OGB-1AM passively diffuses into cells through the plasma membrane and is converted to OGB-1 by intracellular esterase. OGB-1 fluorescence images were compared with post hoc staining with fluorescent Nissl, a neuron-specific marker (Fig. 1, top). Two-photon microscopic observation revealed that the loading efficiency gradually decreased as the Z depth increased and became almost zero at a depth of 100 µm underneath the surface of the slice preparation (Fig. 1, bottom). However, in case of neurons located within a depth of 50 µm, 88.3 ± 2.5% cells were labeled with OGB-1AM (n = 4 slices).
|
) and that OGB-1 was homogenously distributed into the cytoplasmic space, we estimated the intracellular concentrations of OGB-1 in the AM-loaded neurons and found that they ranged from 7 to 50 µM (shaded area of Fig. 2A, right).
|
; Thomas et al. 2000). Thus the loaded OGB-1 may function as a [Ca2+]i reporter and as a calcium chelator. To examine whether OGB-1AM loading disturbs the nature of neuronal firing activity, we performed loose-patch recordings from randomly selected AM-loaded neurons and recorded spontaneously occurring action potentials (Fig. 2B). The average firing rate did not differ significantly between the OGB-1-loaded and unloaded cells (Fig. 2B, middle); moreover, the distribution of the interspike intervals also did not differ significantly between these two groups (Fig. 2B, right). In addition, we carried out whole cell voltage-clamp recording to record spontaneous synaptic inputs (Fig. 2, C and D, top). OGB-1AM loading did not alter the mean event rate, the amplitude of spontaneous excitatory or inhibitory postsynaptic events (Fig. 2, C and D, middle), or the distribution of the amplitudes and the interevent intervals of the postsynaptic events (Fig. 2, C and D, bottom). These results suggest that OGB-1AM loading per se does not alter the level or pattern of neuronal electrical activity. Relationship between action potentials and somatic calcium spikes
Simultaneous recordings of membrane potential and somatic calcium fluorescence showed that somatic calcium transients strictly reflected the action potentials (Fig. 3 A, left), whereas somatic fluorescence did not change with subthreshold fluctuations in the membrane potential (Fig. 3A, right). This implies that the timings of the action potentials can be reconstructed based on the onset timings of individual calcium transients without being disturbed by subthreshold synaptic inputs or ongoing membrane fluctuations.
|
F/F amplitude was decreased to 4.8 ± 10.6% in the Cd2+-treated neurons (n = 5). Thus the calcium transients appeared to depend on extracellular calcium influx through voltage-dependent calcium channels. Consistent with this, calcium transients did not occur in a calcium-free solution (Fig. 3B, right). The F/F amplitude was decreased to 1.2 ± 0.9% in the calcium-free neurons (n = 4).
We also examined whether calcium release from endogenous Ca2+ stores contributes to the calcium transients (Fig. 3C). Neurons were treated for >30 min with thapsigargin, a Ca2+-ATPase inhibitor, to deplete calcium in the endoplasmic reticulum. Thapsigargin did not significantly alter the amplitude of the calcium transients. The F/F amplitude was 5.4 ± 1.3% in the control and 5.0 ± 1.7% in thapsigargin-treated neurons (n = 4). However, thapsigargin prolonged the recovery of the calcium transients. The decay time constant was 484 ± 123 ms in the control and 6,750 ± 2,217 ms in the thapsigargin-treated neurons. These results indicate that calcium release from the internal stores is not required for the rapid surge of a calcium transient; however, thereafter, the intercellular Ca2+-ATPase-dependent calcium clearance, at least in part, contributes to the pattern of calcium decay.
We next addressed the relationship between the number of action potentials in a burst and somatic calcium increase. All data were collected from the calcium transients obtained during spontaneous activity. As shown in Fig. 4A, single spikes evoked clearly visible calcium transients, whereas at frequencies of >5 Hz, the individual spikes in bursts were inseparable in the calcium traces and instead evoked single large events due to the temporal accumulation of calcium transients owing to their slow decay kinetics.
The amplitude of calcium transients increased as a function of the average spike counts (Fig. 4B, left, red circles); however, it varied largely between the transients even if the transients had the same number of spikes (black dots). The decay time constant after calcium transients was not significantly different among neurons (n = 10 cells, data not shown). The decay also did not depend on the number of spikes involved in the events (Fig. 4B, right). The variance of the amplitudes appeared to arise, at least in part, from the intraburst spike timings because the sizes of the calcium transients also correlated positively with the spike frequencies (Fig. 4C). Figure 4D depicts the sizes of the calcium transients on a pseudocolor scale in dimensions of spike numbers versus firing rates, indicating that the transient size depends on both parameters, that is, the same amplitude of calcium transients can be evoked by different sets of spike numbers and firing rates.
Conditioning of the spike detection algorithm with PCA and SVM
We developed a novel method to automatically detect the spike events using a machine learning algorithm. Although in the following analysis, we present results obtained from datasets recorded at a sampling rate of 10 Hz, similar results were obtained in the range from 10 to 50 Hz. In the first step, a part of the calcium trace was regarded as a time-series vector (Fig. 5A, top, see METHODS) and was decomposed into two dimensions by PCA. Data were plotted in a space of the first PC versus the second PC. For illustrative purposes, 1,782 randomly selected spike vectors and 2,000 nonspike vectors obtained from 10 cells are shown in Fig. 5B. The vectors with spikes (colored dots) and those without spikes (gray dots) tended to be scattered in different regions.
We attempted to determine the appropriate vector length, i.e., the length of the fluorescence trace segments around the focused spikes that should be clipped out of a parent trace. The optimal length is the length that yields the best separation between spike and nonspike vectors. We computed the JS divergences, which assess the degree of separation, by performing the entire PCA procedure against various combinations of the start and end time points, i.e., ts and te, respectively, relative to the focused spikes (Fig. 5A). The JS divergence peaked when the vectors were extracted from ts = –200 ms (start) to te = +400 ms (end; Fig. 5A, bottom). In the following analysis, we used vectors with ts = –200 ms and te = +400 ms.
We used linear SVM, a supervised machine learning algorithm, to determine the cutoff line that best separated the spike and nonspike vectors in the PC coordinate system. As the SVM is conditioned to judge whether the vectors contained spikes or not, it gradually learns to identify vectors with spikes. The average learning curve is shown in Fig. 5, C and D. In this analysis, the vectors used for SVM conditioning were not used for the subsequent detection tests. Bursts at spike rates >5 Hz were regarded as single events, and one frame error was allowed around the actual event time. We considered two types of errors: erroneous detection of a nonspike as a spike (false-positive) and erroneous oversight of a spike as a nonspike (false-negative). Both types of errors decreased as the number of vectors used for conditioning increased (Fig. 5C), and the learning was almost saturated at conditioning with 1,000 vectors (Fig. 5D).
We also conditioned SVM without PCA preprocessing of the vectors, that is, the original high-dimensional vectors were directly used for SVM conditioning. In this case, the total computation time spent for conditioning was 50–100% longer as compared with the time spent with the PCA-SVM algorithm, and the error rates after learning were 10–20% higher (data not shown). Thus the data compression with PCA prior to SVM conditioning enhances the learning efficacy of SVM.
Fast and accurate reconstruction of spike timings from calcium signals
The SVM score (see METHODS) quantifies the distance from a given vector to the cutoff line that separates the spike and nonspike vectors, representing the likelihood that the vector contains spike(s). Spike times are determined as the >0 local maxima of the SVM score. The representative fluorescence trace from two neurons and their corresponding SVM scores are shown in Fig. 6. Note that these traces were obtained from neurons that had not been used in SVM conditioning. Spike times detected automatically with the PCA-SVM algorithm are indicated (
along the SVM score). They corresponded well, although not perfectly, to the actual times of the spikes monitored by loose-patch recording (Fig. 6, A and B, bottom). The error rates are shown in each top right panel. We compared the detection results between the PCA-SVM algorithm and four trained human operators in our laboratory. In our slice preparations, 
70% of the neurons generated stereotypical calcium transients with high signal-to-noise (SN) ratios, as shown in Fig. 6A (SN ratio = 48). In these cases, the detection error rates by both our algorithm and by the human operators were low (Fig. 6A). Other neurons, however, exhibit obscure calcium transients, presumably because of the high firing rates or out-of-focus signals as shown in Fig. 6B (SN ratio = 12). In these cases, the false-positive and false-negative error rates increased to 40% in the case of the human operators; however, the PCA-SVM algorithm could still find spikes with error rates of <10%. The bottom right histograms represent the distributions of the detected events around the actual spike timings, indicating that the algorithm determined the timings of 40–60% events in the correct frames. Moreover, the PCA-SVM algorithm and human operators had different working speeds. Even in the "easy" case shown in Fig. 6, the human operators required 188 ± 49 s to complete spike detection, whereas the algorithm completed the task in 14 ms with a mass-produced 1-GHz desktop computer.
|
We next compared the spike detection power of our algorithm with that of the other existing methods. We employed two representative algorithms, i.e., template matching (Kerr et al. 2005) and deconvolution (Yaksi and Friedrich 2006). Both algorithms were run under the assumption of a calcium decay constant of 500 ms (see Fig. 4B). All calculations were done in accordance with the previous papers except that no image compensations (i.e., background subtraction, local averaging or filtering) were performed in advance. Their scores are shown in Fig. 7. In the template-matching and deconvolution algorithms, we had to arbitrarily determine a threshold for spike detection. We defined them to minimize the error rates for individual trace. This optimization process could be disadvantageous as compared with our entirely automatic algorithm because all parameters in our algorithm were maintained across traces and not optimized for every trace. Even in these cases, our algorithm showed better spike detection rates than those the template-matching and deconvolution algorithms (Fig. 7). The most plausible reason seemed to be that these methods more frequently picked incorrect frames before or after actual spike timings (>2 frames) compared with PCA-SVM algorithm (right histogram). Similar results were obtained in other six neurons. Incidentally, the computation time did not differ much among these algorithms.
|
) (Fig. 8). The Z1 and Z2 planes contained 127 and 91 neurons, respectively (Fig. 8B). A rasterplot was reconstructed using the PCA-SVM algorithm (Fig. 8C). With the automatic algorithm, the time spent for reconstructing the whole network activity was reduced from a few hours (manual) to a few seconds (automatic).
|
|
|
DISCUSSION |
|---|
|
90% of the Nissl-positive cells within a distance of 50 µm from the slice surface were loaded with OGB-1AM. Thus OGB-1AM permeated through the brain tissues up to a depth of 50 µm, which happens to be almost equal to the Z depth accessible with a one-photon laser beam used in spinning-disk confocal microscopy. The intracellular concentration of AM-loaded OGB-1 seemed to be tens of micromoles. Although this concentration was enough to detect single action potentials, it did not seem to alter neuronal excitability. Suprathreshold activity induced calcium transients, whereas subthreshold synaptic activity alone did not seem to elicit calcium elevation in the cell body. This is probably because synaptic activity occurs at synaptic sites that are away from the cell body, whereas action potentials are initiated in the vicinity of cell body.
Because of the slow decay of the calcium transients, a series of action potentials with narrow interspike intervals produces calcium accumulation that overlaps the decay of previous calcium spikes (Canepari et al. 1999; Helmchen et al. 1996). Some studies have attempted to reconstruct spike counts (or frequencies) from raw F/F signals. This requires an assumption that the calcium transient amplitudes strictly correlate with the spike counts (Feinerman and Moses 2006; Murayama et al. 2005). In general, however, neurons emit burst-like spike trains with variable spike counts and frequencies, and we found that both the spike count and frequency influence calcium dynamics in a nonlinear intermixed manner. Thus even if we consider the entire changes of F/F, one cannot simultaneously know the firing rate and the number of spikes within a burst (<5 Hz), at least at the frame rates (10–50 Hz).
The spike reconstruction processes used in fMCI experiments has practical problems. The most elementary method to detect the neuronal events is by visual inspection. This manual operation is time consuming, laborious and may be subjective. As we demonstrated, human eyes are indeed inaccurate and are often biased, inevitably producing errors. To improve the detection process, we have created a new algorithm that focuses on specific segments around the peaks of F/F signals and picks up spike events with the help of a combination of PCA and SVM. The spike detection power of this algorithm was maximal when the fluorescence trace segments were sampled from ts = –200 ms to te = +400 ms relative to the focused frame, i.e., the assumed spike timings. The te value is reasonably similar to the decay constant of the calcium transients.
Not only was the computation time of the PCA-SVM algorithm >10,000 times shorter than that of the manual computation performed by human operators, but the error of the PCA-SVM algorithm was also a few times smaller than that of manual computation. This implies that manual processes are unnecessary and should be excluded as much as possible. The errors committed by our algorithm were fewer than those by template-matching (Kerr et al. 2005) and deconvolution (Yaksi and Friedrich 2006). Unlike template-matching, our method takes both the absolute F/F amplitude of the calcium transient and its stereotyped decay into consideration. The dual parameters are thought to improve the detection power. Deconvolution may be suitable for reconstructing the firing rate in the neurons that emit continuous spikes at frequencies of >10 Hz and have long decay constants of calcium transients (3–6 s) (Yaksi and Friedrich 2006). But in mammalian excitatory cells such as hippocampal neurons, which usually generate temporally sparse (<1 Hz) firing activities and a short calcium decay constant (0.5–1 s), deconvolution may fail to detect precise spikes. A more crucial difference between these methods and ours, however, is the degree of subjective factors. In the template-matching and deconvolution algorithm, one needs to empirically define a threshold to extract neuronal events. This manual process is quite arbitrary and is subject to human bias. In this regard, our algorithm automatically finds the optimal line that separates the spikes during SVM conditioning, and the SVM score is defined in order that the detection threshold is zero. On the other hand, this could also be considered as a drawback of our algorithm—one first needs to condition the algorithm with at least many signals (we used 1,000) and thus has to prepare these fluorescence traces in advance.
As hippocampal neurons in cultured slices showed relatively homogenous calcium dynamics (for example, the decay time constant was similar among neurons), the parameters tuned with datasets of only 10 sample cells could be applied to detection for other neurons. But it should be noted that the parameters optimized in our study may not be directly applicable to other experimental systems that include different brain regions or different preparations. The PCA-SVM algorithm itself, however, is simple enough that one can easily optimize the parameters. The Matlab code of SVM is freely available at the website described in the Methods. Please contact the corresponding author (T. Sasaki; e-mail: ff077204@mail.ecc.u-tokyo.ac.jp) for the parameters used in this study. Finally, we believe that this automatic algorithm does not merely enhance the applicability of fMCI but also may help signal detection in other on-line experiments.
|
|
GRANTS |
|---|
|
|
|
ACKNOWLEDGMENTS |
|---|
|
|
|
FOOTNOTES |
|---|
Address for reprint requests and other correspondence: T. Sasaki, Laboratory of Chemical Pharmacology, Graduate School of Pharmaceutical Sciences, The University of Tokyo, Tokyo 113-0033 Japan (E-mail: ff077204{at}mail.ecc.u-tokyo.ac.jp)
|
|
REFERENCES |
|---|
|
Cossart R, Aronov D, Yuste R. Attractor dynamics of network UP states in the neocortex. Nature 423: 283–288, 2003.[CrossRef][Web of Science][Medline]
Crepel V, Aronov D, Jorquera I, Represa A, Ben-Ari Y, Cossart R. A parturition-associated nonsynaptic coherent activity pattern in the developing hippocampus. Neuron 54: 105–120, 2007.[Medline]
Dombeck DA, Khabba AN, Collman F, Adelman TL, Tank DW. Imaging large-scale neural activity with cellular resolution in awake, mobile mice. Neuron 56: 43–57, 2007.[CrossRef][Web of Science][Medline]
Feinerman O, Moses E. Transport of information along unidimensional layered networks of dissociated hippocampal neurons and implications for rate coding. J Neurosci 26: 4526–4534, 2006.
Göbel W, Kampa BM, Helmchen F. Imaging cellular network dynamics in three dimensions using fast 3D laser scanning. Nat Method 4: 73–79, 2007.[CrossRef]
Greenberg DS, Houweling AR, Kerr JN. Population imaging of ongoing neuronal activity in the visual cortex of awake rats. Nat Neurosci 11: 749–751, 2008.[CrossRef][Web of Science][Medline]
Helmchen F, Imoto K, Sakmann B. Ca2+ buffering and action potential-evoked Ca2+ signaling in dendrites of pyramidal neurons. Biophys J 70: 1069–1081, 1996.[Web of Science][Medline]
Ikegaya Y, Aaron G, Cossart R, Aronov D, Lampl I, Ferster D, Yuste R. Synfire chains and cortical songs: temporal modules of cortical activity. Science 304: 559–564, 2004.
Ikegaya Y, Le Bon-Jego M, Yuste R. Large-scale imaging of cortical network activity with calcium indicators. Neurosci Res 52: 132–138, 2005.[CrossRef][Web of Science][Medline]
Kerr JN, Greenberg D, Helmchen F. Imaging input and output of neocortical networks in vivo. Proc Natl Acad Sci USA 102: 14063–14068, 2005.
Kerr JN, de Kock CP, Greenberg DS, Bruno RM, Sakmann B, Helmchen F. Spatial organization of neuronal population responses in layer 2/3 of rat barrel cortex. J Neurosci 27: 13316–13328, 2007.
Koyama R, Muramatsu R, Sasaki T, Kimura R, Ueyama C, Tamura M, Tamura N, Ichikawa J, Takahashi N, Usami A, Yamada MK, Matsuki N, Ikegaya Y. A low-cost method for brain slice cultures. J Pharmacol Sci 104: 191–194, 2007.[CrossRef][Web of Science][Medline]
Lips MB, Keller BU. Activity-related calcium dynamics in motoneurons of nucleus hypoglossus from mouse. J Neurophysiol 82: 2936–2946, 1999.
MacLean JN, Watson BO, Aaron GB, Yuste R. Internal dynamics determine the cortical response to thalamic stimulation. Neuron 48: 811–823, 2005.[CrossRef][Web of Science][Medline]
Mao BQ, Hamzei-Sichani F, Aronov D, Froemke RC, Yuste R. Dynamics of spontaneous activity in neocortical slices. Neuron 32: 883–898, 2001.[CrossRef][Web of Science][Medline]
Markram H, Helm PJ, Sakmann B. Dendritic calcium transients evoked by single cavk-propagating action potentials in rat neocortical pyramidal neurons. J Physiol 485: 1–20, 1995.
Moreaux L, Laurent G. Estimating firing rates from calcium signals in locust projection neurons in vivo. Front Neural Circuits 1: 2, 2007.[Medline]
Morita M, Higuchi C, Moto T, Kozuka N, Susuki J, Itofusa R, Yamashita J, Kudo Y. Dual regulation of calcium oscillation in astrocytes by growth factors and pro-inflammatory cytokines via the mitogen-activated protein kinase cascade. J Neurosci 23: 10944–10952, 2003.
Murayama M, Miyazaki K, Kudo Y, Miyakawa H, Inoue M. Optical monitoring of progressive synchronization in dentate granule cells during population burst activities. Eur J Neurosci 21: 3349–3360, 2005.[CrossRef][Web of Science][Medline]
Ohki K, Chung S, Ch'ng YH, Kara P, Reid RC. Functional imaging with cellular resolution reveals precise micro-architecture in visual cortex. Nature 433: 597–603, 2005.[CrossRef][Web of Science][Medline]
Ohki K, Chung S, Kara P, Hubener M, Bonhoeffer T, Reid RC. Highly ordered arrangement of single neurons in orientation pinwheels. Nature 442: 925–928, 2006.[CrossRef][Web of Science][Medline]
Ramdya P, Reiter B, Engert F. Reverse correlation of rapid calcium signals in the zebrafish optic tectum in vivo. J Neurosci Methods 157: 230–237, 2006.[CrossRef][Web of Science][Medline]
Sasaki T, Kimura R, Tsukamoto M, Matsuki N, Ikegaya Y. Integrative spike dynamics of rat CA1 neurons: a multineuronal imaging study. J Physiol 574: 283–290, 2006.
Sasaki T, Matsuki N, Ikegaya Y. Metastability of active CA3 networks. J Neurosci 27: 517–528, 2007.
Sato TR, Gray NW, Mainen ZF, Svoboda K. The functional microarchitecture of the mouse barrel cortex. PLoS Biol 5: e189, 2007.[CrossRef][Medline]
Smetters D, Majewska A, Yuste R. Detecting action potentials in neuronal populations with calcium imaging. Methods 18: 215–221, 1999.[CrossRef][Web of Science][Medline]
Smola A, Schölkopf B. A tutorial on support vector regression. Stat Comput 14: 199–222, 2004.[CrossRef]
Sohya K, Kameyama K, Yanagawa Y, Obata K, Tsumoto T. GABAergic neurons are less selective to stimulus orientation than excitatory neurons in layer II/III of visual cortex, as revealed by in vivo functional calcium imaging in transgenic mice. J Neurosci 27: 2145–2149, 2007.
Stosiek C, Garaschuk O, Holthoff K, Konnerth A. In vivo two-photon calcium imaging of neuronal networks. Proc Natl Acad Sci USA 100: 7319–7324, 2003.
Takahashi A, Camacho P, Lechleiter JD, Herman B. Measurement of intracellular calcium. Physiol Rev 79: 1089–1125, 1999.
Takahashi N, Sasaki T, Usami A, Matsuki N, Ikegaya Y. Watching neuronal circuit dynamics through functional multineuron calcium imaging (fMCI). Neurosci Res 58: 219–225, 2007.[CrossRef][Web of Science][Medline]
Thomas D, Tovey SC, Collins TJ, Bootman MD, Berridge MJ, Lipp P. A comparison of fluorescent Ca2+ indicator properties and their use in measuring elementary and global Ca2+ signals. Cell Calcium 28: 213–223, 2000.[CrossRef][Web of Science][Medline]
Yaksi E, Friedrich RW. Reconstruction of firing rate changes across neuronal populations by temporally deconvolved calcium imaging. Nat Method 3: 377–383, 2006.[CrossRef]
This article has been cited by other articles:
|
|
 |
|
  T. Sasaki, G. Minamisawa, N. Takahashi, N. Matsuki, and Y. Ikegaya Reverse Optical Trawling for Synaptic Connections In Situ J Neurophysiol, July 1, 2009; 102(1): 636 - 643. [Abstract] [Full Text] [PDF]
|
|
| ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| HOME | HELP | FEEDBACK | SUBSCRIPTIONS | ARCHIVE | SEARCH | TABLE OF CONTENTS |
| Visit Other APS Journals Online |
TOP
ABSTRACT
INTRODUCTION
) and by manual computation (
), template matching (
). For details, see the legend of 