Radially expanding transglial calcium waves
in the intact cerebellum
Tycho M. Hooglanda,b,1,2, Bernd Kuhna,b,1,2, Werner Go ¨belc, Wenying Huanga, Junichi Nakaid,3, Fritjof Helmchenc,
Jane Flinta, and Samuel S.-H. Wanga,b,2
aDepartment of Molecular Biology andbPrinceton Neuroscience Institute, Princeton University, Lewis Thomas Laboratory, Washington Road,
Princeton, NJ 08544;cBrain Research Institute, University of Zu ¨rich, Winterthurerstrasse 190, 8057 Zu ¨rich, Switzerland; anddLaboratory for
Memory and Learning, RIKEN Brain Science Institute, 2-1, Hirosawa, Wako-shi, Saitama 351-0198, Japan
Edited by Charles F. Stevens, The Salk Institute for Biological Studies, La Jolla, CA, and approved January 14, 2009 (received for review September 16, 2008)
Multicellular glial calcium waves may locally regulate neural activity
or brain energetics. Here, we report a diffusion-driven astrocytic
in a confined volume without fully encompassing any one cell. By
using 2-photon microscopy in rodent cerebellar cortex labeled with
discovered spontaneous calcium waves that filled approximately
ellipsoidal domains of Bergmann glia processes. Waves spread in 3
during expansion, and were reversibly blocked by P2 receptor antag-
onists. Consistent with the hypothesis that ATP acts as a diffusible
trigger of calcium release waves, local ejection of ATP triggered P2
Transglial waves represent a means for purinergic signals to act with
local specificity to modulate activity or energetics in local neural
astrocytes ? Bergmann glia ? in vivo ? 2-photon microscopy ? G-CaMP2
cell to cell, as demonstrated in a variety of explanted central
nervous system tissues, including cell culture (1–3), retina (4), and
neocortical brain slices (5).
Advances in optical imaging methods have allowed astrocytic
calcium signals to be imaged in vivo. Astrocytic signals occur
spontaneously in the neocortex (6, 7) and can be evoked by
significance for normal function. In all cases, the observed signals
have occurred in well-defined populations of a few astrocytes at
Under some circumstances, calcium signals also spread in a
wave-like fashion across many glial cells. In the retina, focal
stimulation can trigger spreading astrocytic waves (4). Spreading
astrocytic waves can be triggered by focal electrical stimulation in
brain slices (10) and by ATP release in culture (3, 11). Glial waves
have been observed in radial glia in the developing neocortex (12)
and in models of spreading depression (13–15).
We examined astrocytic signaling in the cerebellum in vivo,
which has not been characterized previously. We used in vivo
2-photon microscopy in combination with either bolus loading of
calcium indicators or expression of the genetically encoded
calcium sensor protein G-CaMP2 targeted to Bergmann glia
(BG), the astrocytes of the molecular layer (ML). In brain slices,
BG mobilize calcium in response to a number of neurotrans-
mitters (16, 17) and can generate subcellular domains of calcium
release in response to synaptic stimulation via activation of
purinergic receptors (18, 19).
Here, we report that BG calcium release can be organized into
highly symmetric waves. We characterize these waves in 3 dimen-
sions and show that they form near-ellipsoidal domains that span
internal stores. Astrocytic calcium signals can also spread from
calcium signals in vivo we performed 2-photon laser scanning
microscopy on cerebellar folia crus I and II in anesthetized rats and
1.0 ?M), visible structures in the ML were brightly labeled glial
identified as BG palisades by their orientation along the parallel
fiber (PF) axis and by the fact that they arose from numerous
appendages sprouting from larger main processes (22) (Fig. 1A,
supporting information (SI) Movie S1). This labeling pattern was
confirmed by photoconversion of fluo-4 and fluo-5F to electron-
dense products for examination by transmission electron micros-
an unusual widespread type of spontaneous calcium signal in the
then expanded radially to encompass multiple BG stem processes
and their appendages (Fig. 1B, Movie S2). In total we analyzed 108
spontaneous calcium wave events in 22 rats, and 23 spontaneous
calcium wave events in 11 mice.
Three-Dimensional Characterization of Transglial Calcium Waves. The
mean fluorescence change reached or exceeded 10% of the peak
value, was 11 ? 5 s (range, 3–22 s) in rats, comparable to signals
previously observed in vitro (18). Within the normal xy-imaging
plane signals filled approximately elliptical domains with a mean
was reached within an expansion time of 4.2 ? 2.1 s.
The elliptical appearance of domains spanning multiple BG
suggested that they were mediated by a diffusible extracellular
signal emanating from a single source. Consistent with diffusion,
Dapp of the expanding area A, calculated by using the relation
Dapp ? A/4t, was 165 ? 11 ?m2/s (mean ? SEM). Diffusion-
mediated spread should be anisotropic because extracellular diffu-
sion in the ML is ?1.4-fold faster in the PF axis than in the
perpendicular direction (24). Consistent with this, transglial do-
Author contributions: T.M.H., B.K., W.G., F.H., and S.S.-H.W. designed research; T.M.H.,
B.K., and W.G. performed research; T.M.H., B.K., W.G., W.H., J.N., F.H., and J.F. contributed
new reagents/analytic tools; T.M.H. and B.K. analyzed data; and T.M.H., B.K., F.H., and
S.S.-H.W. wrote the paper.
The authors declare no conflict of interest.
This article is a PNAS Direct Submission.
1T.M.H. and B.K. contributed equally to this work.
2To whom correspondence may be addressed. E-mail: firstname.lastname@example.org, bkuhn@
princeton.edu, or email@example.com.
3Present address: Saitama University Brain Science Institute, 255 Shimo-Okubo, Sakura-ku,
Saitama City, Saitama 338-8570, Japan.
This article contains supporting information online at www.pnas.org/cgi/content/full/
March 3, 2009 ?
vol. 106 ?
mains had an average major-to-minor axis ratio of 1.3 ? 0.2, major
and minor axis lengths of 37 ? 13 and 29 ? 12 ?m, and were
in a second set of experiments we used ‘‘arbitrary plane imaging’’
(25). Rat cerebellar cortex was bolus-loaded with OGB-1/AM and
scanned in an xz parasagittal plane, parallel to Purkinje cell (PC)
dendritic arbors and perpendicular to the PF axis (Fig. 1F, Movie
1G; Table S1). Domains were oriented along the pia-granule cell
layer axis (deviation ? ? 4 ? 12°, Fig. 1H) with a major-to-minor
axis ratio of 1.5 ? 0.2 (Fig. 1G). Anisotropy coincides with the
that signals may spread or be amplified within individual BG.
Spread of Calcium Waves Through Bergmann Glia. To visualize trans-
glial waves more clearly in BG we used the nonreplicating adeno-
virus AdEasy-1 (26) to express the calcium-sensitive fluorescent
protein G-CaMP2. When injected into the mouse cerebellar cortex
in vivo, this adenovirus infected only glial cells, consistent with in
were possible to a depth of 230 ?m in the 2 main astrocyte
populations, BG (Fig. 2A) and velate astrocytes in the granule cell
layer. By varying the amount and depth of virus injection and the
time after infection we obtained infection patterns ranging from
sparse labeling of individual BG (Fig. 2A, Movie S4) to complete
labeling in a region ?250 ?m wide. Between 1 and 25 days
postinfection no dead cells or changes in tissue appearance or BG
morphology (compared with GFP-GFAP mice) were observed.
ML (Fig. 2B, Movie S5), with fluorescence changes of up to 93%
above baseline in individual processes. Domains were oriented
Compared with MCBL-loaded rat cerebellum, domains were
0.001, 2-tailed t test) and briefer (6 ? 2 s, P ? 0.001, 2-tailed t test),
perhaps reflecting the high cooperativity of G-CaMP2 for calcium
(Hill coefficient ? 3.8). In addition, velate astrocytes also showed
?m below the Purkinje cell layer, indicating that they are triggered
in the granular layer. Velate cell waves had an expansion time of
2.5 ? 0.4 s, lasted 10.4 ? 3.3 s, and had a diameter of 49 ? 12 ?m.
We estimated the number of BG cells and processes encom-
passed by the domain of a single transglial wave. Reconstructed
image stacks from GFAP-GFP mice had a density of one BG per
overlies 1,500/84 ? 18 BG cells, and assuming 4 processes per BG,
72 ? 28 processes. However, the processes in a domain come from
(28), BG interdigitate with one another in the ML. In tissue that
expressed G-CaMP2 sparsely (Fig. 2A, Movie S4), processes from
individual BG spanned regions measuring 40 ? 10 ?m across
parasagittally and 19 ? 3 ?m across in the parallel fiber
direction (3 BG from 3 mice). Thus, processes may originate
from BG somata both directly underlying the domain and in a
surrounding annulus 20 ?m thick parasagittally and 9.5 ?m
longitudinally. The total number of BG somata contained in
Orientation relative to
GCL-pia axis (˚)
Area (103 µm2)
0 s1.0 s2.1 s
3.1 s 4.1 s5.1 s
Orientation relative to
PF axis (˚)
0 10 20 30 40
Distance from centroid
Rate of Spread (µm/s)
show a distinct striate pattern matching lateral protrusions from stem processes of Bergmann glia (BG). (Middle) Maximal side projection showing similarity between
fluo-5F/AM labeling and GFAP-GFP expression. (Bottom) Optical sections taken from the Purkinje cell layer, with BG somata arranged around Purkinje cells. (B)
(D) (Left) Wavefront slowing with distance from the initiation site. (Right) Linear rate of increase of wave area, with an average apparent diffusion constant Dapp?
plane orthogonal to the surface of the cerebellum. (G) Wave orientation along the axis of BG stem processes. (H) Distribution of wave orientation relative to the
pia–Purkinje cell axis.
Transglial calcium waves in the cerebellar cortex in vivo. (A) Staining patterns of the cerebellar cortex bolus-loaded with fluo-5F/AM (rat) or expressing GFP
Hoogland et al.
March 3, 2009 ?
vol. 106 ?
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this larger effective domain is 51 ? 11 cells, all of which
potentially contribute to the transglial wave.
Spontaneous Subcellular Glial Calcium Signals.Inadditiontowaveswe
also observed subcellular calcium transients in G-CaMP2-
expressing BG that resembled microdomains previously described
5.5 ? 1.6 ?m wide and lasted 2.4 ? 0.8 s (18 events in 5 mice, Fig.
S1 A and B). In velate astrocytes the transients occurred mainly in
processes, had a diameter of 7.6 ? 1.9 ?m, and lasted 2.6 ? 0.8 s
(13 events, 4 mice; Fig. S1C). Subcellular events were also detected
in MCBL experiments but the assignment to specific cellular
structures was not possible because of the low contrast and lack of
Transglial Calcium Waves Recur in the Same Location. The expanding
dynamics of waves suggested that they were triggered at discrete
origination sites. In search of repeated wave origination from the
same site we monitored fields of view in the ML for 14 to 96 min.
Movies contained 2 to 30 events each (Fig. 3A) that often over-
lapped in space (Fig. 3B). If waves originated at random locations,
should be uniformly distributed (Fig. 3C, gray histogram). In
contrast, for actual overlapping pairs, squared distances were
skewed toward short distances (Fig. 3C, red histogram; different
from uniform distribution, P ? 0.01, Kolmogorov–Smirnov test),
consistent with the existence of wave-triggering foci.
Extended monitoring also allowed us to test whether waves were
triggered by laser illumination (30). Events appeared at a uniform
rate of 0.40 ? 0.13 waves per minute of observation (Fig. 3D; rate
not correlated with observation time, P ? 0.3, n.s., 2-tailed t test),
suggesting that events are not illumination-induced. Waves could
also initiate outside the FOV and sometimes began before the start
of imaging. Calcium waves were observed under all types of
anesthesia used: urethane, ketamine/xylazine, and isoflurane
(Table S1 and Table S2). Thus, transglial calcium waves occur
spontaneously under a variety of conditions.
10 μm below
1.0 s 1.5 s
Orientation relative to PF axis (˚)
Number of BGs
wave domain. (D) Orientation of domains relative to the parallel fiber axis. (E) Distribution of domain sizes relative to a single BG.
0 s131 s
of event pairs
Event rate (min-1)
distance (103 μm2)
Normalized event rate
with fluo-5F. (B) Two example events. (C) The distribution of squared center-to-
center distances between different events (red) differs from random expecta-
tions (Monte Carlo model; gray). (D) Constancy of the rate of transglial wave
events during long-term imaging, averaged ?8 fields of view. (E) The rate of
spontaneous transglial calcium waves during topical application of PPADS (500
?M) and suramin (1 mM) and after washout (wash), normalized to control.
Recurrence of transglial calcium waves at the same location. (A) Loca-
www.pnas.org?cgi?doi?10.1073?pnas.0809269106 Hoogland et al.
Spontaneous Transglial Calcium Waves Are Reversibly Blocked by P2
Receptor Antagonists. BG express a variety of G protein-coupled
receptors that couple to calcium release from intracellular stores
(17, 31), including P2Y receptors, which are activated by ATP (16,
18, 19). To test whether spontaneous transglial waves rely on a
purinergic receptor-dependent mechanism, we imaged transglial
waves in rats before, during, and after surface application of the P2
The rate of spontaneous events as measured with Fluo-5F was
7 ? 12% for suramin (n ? 3), respectively (Fig. 3E; P ? 0.01,
the brain surface with saline, the rate fully recovered to 96 ? 17%
and 83 ? 17% of control (Fig. 3E, PPADS, P ? 0.01, suramin, P ?
0.05, 2-tailed tests).
Local ATP Injection Triggers Radially Expanding Transglial Waves. The
ability of purinergic receptor antagonists to block spontaneous
waves suggests that local release of ATP could trigger calcium
waves. To test this possibility we pressure-ejected ATP from a
pipette placed in the ML of rats and mice loaded with fluo-5F/AM
or mice expressing G-CaMP2. In all cases, ATP evoked spreading
calcium waves similar to spontaneous waves (Fig. 4A, Movie S7;
Table S1, Table S3). Filled elliptical domains (Fig. 4B) had similar
orientation (rat Fluo-5F, P ? 0.8; mouse Fluo-5F, P ? 0.7; mouse
G-CaMP2, P ? 0.9, 2-tailed t test) and major-to-minor axis ratio as
spontaneous waves (rat Fluo-5F, P ? 0.7; mouse Fluo-5F, P ? 0.3;
mouse G-CaMP2, P ? 0.7; 2-tailed t test). No calcium waves were
triggered by pressure ejection of saline (3 mice). ATP-triggered
waves filled regions that were larger and more variable than
spontaneous waves (19,000 ? 8,000 ?m2, range 7,800–30,600 ?m2,
(700–3,000 ?m2/s). Dappwas correlated with the size of the re-
sponding region (rank correlation, ?1.0), suggesting that signaling
mechanisms may have been saturated by the amount of ATP
injected or that pressure ejection introduced a nondiffusive com-
ponent to the wave spread.
To examine the 3-dimensional geometry of ATP-triggered
waves, ATP was injected repeatedly at one location and calcium
changes were imaged at different depths. Waves were visible at a
4C). ATP injection at the pial surface and in the molecular and
Purkinje cell layers could trigger waves. Injection in the lower third
of the ML spread to underlying Purkinje cell somata (Movie S8)
and velate astrocytes (Fig. 4D). Thus, all of the depths at which
waves originate and propagate are sensitive to ATP.
We used ATP to further probe the properties of spreading
calcium events. As was observed for spontaneous events, applica-
tion of PPADS (500 ?M) to the brain surface reduced the ampli-
tude of ATP-triggered signals by 53 ? 30% (P ? 0.05, n ? 3) from
control (Fig. 4E), consistent with a P2 receptor-dependent mech-
anism. P2 receptor activation triggers calcium release from internal
stores (19, 32), which after activation can be refractory for tens of
seconds as refilling occurs (33). We delivered 5 successive ATP
to 23 ? 4% (rat, fluo-5F, n ? 4), 33 ? 4% (mouse, fluo-5F, n ?
4), and 11 ? 2% (mouse, G-CaMP2, n ? 4) of the size of the first
response. At 120-s intervals the amplitude of the fifth response was
undiminished at 100 ? 16% (rat, fluo-5F), 100 ? 7% (mouse,
fluo-5F), and 99 ? 3% (mouse, G-CaMP2) of the first response.
Responses recovered to half the size of the first response in an
1.53 s2.05 s
2.56 s3.07 s
-0.51 s0 s
Y (290 µm)
X (290 µm)
ATP + Alexa 594
1 2 3 4 5
1 2 3 4 5
1 2 3 4 5
Mouse (Fluo-5F) Mouse (G-CaMP2)
500 µM PPADS
the molecular layer. Green, Fluo-5F calcium signal; red, Alexa 594 and SR101. (B) Elliptical domain oriented along the PF axis in an ATP-triggered wave. (C) Waves
successive calcium responses after repeated application of ATP. (G) Dependence of response amplitude after 5 pulses of ATP injected at different time intervals.
ATP-triggered transglial calcium waves in vivo. (A) A transglial calcium wave evoked by ejection of ATP (pipette concentration: 1 mM, 10 ms, 0.07 bar) into
Hoogland et al.
March 3, 2009 ?
vol. 106 ?
no. 9 ?
estimated 27 ? 9 s (rat, fluo-5F), 30 ? 6 s (mouse, fluo-5F), and
37 ? 4 s (mouse, G-CaMP2), consistent with refilling times for
internal stores. These results are consistent with a mechanism in
which point-like release of ATP acts on P2 receptors to trigger
transcellular calcium release waves.
This work represents the first demonstration in the intact brain
of intercellular calcium waves triggered by purinergic mecha-
nisms. The occurrence of spontaneous calcium waves encom-
passing multiple BG processes within a defined volume repre-
sents a means for normal tissue to generate a regional signal.
Subcellular and Spreading Events. Our observation of spontaneous
in other brain regions in vivo, where signals tend not to spread
between neighbors, are unresponsive to purinergic receptor block-
ers, and have functionally nonoverlapping domains (9, 34).
Subcellular signals coexisted in the same tissue with more
widespread signals spanning dozens of processes in well-delimited,
approximately ellipsoidal spaces. Resolution and assignment of
signals to BG cellular processes was made possible by the use of
G-CaMP2. G-CaMP2 also provided a means of obtaining mea-
surements without acute introduction of a dye-containing elec-
trode, which could damage tissue. The fact that a less invasive
approach yielded repeated ellipsoidal waves indicates that they are
not pathological, unlike spreading depression, another wave-like
phenomenon seen in neocortical (14, 15) and cerebellar (13)
astrocytes that differs by being independent of purinergic receptor
activation (13), having higher speeds (?15 ?m/s), and a spatial
not restricted to functional domains, because waves with spatially
segregated initiation centers could overlap. Wave domains were
seen throughout the molecular layer, with their major axis in the
transverse plane oriented along the PF axis, whereas the long
axis in the sagittal plane follows the direction of the main
processes of BG. These features suggest that ellipsoidal waves
can be driven repeatedly throughout the molecular layer by
purine release events. Recent reports indicate that in awake
animals, BG signals may occur repeatedly in larger spatial
domains than the current report.†
Origin and Mechanism of Expanding Transglial Waves. Whether the
purinergic triggering signal arises from neurons or glia is currently
unknown. Astrocytes can release ATP in a point-like fashion (11),
opening the possibility that BG or parts thereof could activate
neighboring BG. Such a feedback step could account for why the
slower than the estimated diffusion constant of ATP (200–400
?m2/s) (35), raising the possibility of intermediate cell-to-cell
signaling steps in wave propagation. Another source is molecular
layer interneurons, which can release ATP after parallel fiber
The unusual symmetry of intercellular waves may arise from the
life of 200–500 ms (36) the 2-dimensional full-diameter range of
ATP is 2*(4Dt)1/2? 25–56 ?m, comparable to the range in 2
dimensions of our observed waves and to observations of ATP
spread in cultured astrocytes (3, 11, 37) and ex vivo retinal prep-
The relative contribution of purinergic and gap junction mech-
anisms to intercellular glial signaling is likely to depend on brain
region-specific factors (39). Our observations suggest that in the
cerebellum the size of purinergic sources, as well as their rate of
clearance and breakdown, allow for local spread of calcium waves
to encompass up to dozens of astrocytic processes in vivo. In
neocortex, iontophoretic application of ATP can trigger calcium
yet been reported from neocortex of spontaneous or synaptically
driven ATP-mediated waves. This absence suggests that under
many conditions in the intact neocortex, endogenous ATP release
events may be relatively small or infrequent. Conversely, gap
junction-mediated coupling, a known mechanism for the spread of
glial waves in brain slices (39), may be unfavored in cerebellum
because gap junction coupling between BG is blocked by calcium
Functional Consequences. The downstream effects of transglial cal-
cium waves may include blood flow regulation and energetics,
known to play a role in blood flow regulation (30). Activation of
molecular layer interneurons can cause vasodilation (42). With
could result in the calcium-dependent release of cyclooxygenases
necessary for the local control of blood flow to metabolically active
regions. Interestingly, stimulation of the climbing fiber pathway
causes lactate accumulation originating from BG, an energy source
for metabolically active neurons (43). ATP is also converted to
adenosine, which can offer neuroprotection after transient hypoxia
(44) and affect synaptic plasticity (45). Thus, known glial and
neuronal mechanisms provide several ways in which glial activity
can affect brain function. In the cerebellum, the domain-based
geometry of ellipsoidal waves suggests that these functions may be
organized into groups that are related to one another not just by
connectivity, but also by proximity.
Materials and Methods
Surgery. Procedures were performed in accordance with the guidelines of the
National Institutes of Health and were approved by local authorities (Princeton
University Institutional Animal Care and Use Committee; Cantonal Veterinary
Office Zu ¨rich). Wistar rats (3–6 weeks) or C57/black6 mice (3–4 weeks) were
anesthetized by i.p. injections of either urethane (1.5 g/kg) or a mixture of
ketamine (80 mg/kg) and xylazine (6 mg/kg) (Sigma-Aldrich). Body temperature
was maintained at 37 °C by using a temperature controller and heating blanket
of the lateral cerebellum. In rats the dura was removed. Animals anesthetized
with ketamine and xylazine were either given supporting doses of anesthetic or
anesthetic regulator (LEI Medical).
Multicell Bolus Loading of Calcium Indicators. In vivo bolus loading of indicators
was done as described refs. 20 and 21 with an injection depth of the synthetic
fluorescent calcium indicators Fluo-5F/AM and OGB-1/AM (Invitrogen) 50–100
Adenovirus with G-CaMP2 and Monomeric DsRed Sequence. To overcome the low
inserted at the KpnI site (bp463) of the G-CaMP2 sequence. The resulting fusion
sequence (G-CaMP2?DSRed) was inserted into the replication-incompetent ade-
Viral Infection with G-CaMP2?DSRed. A 0.5-mm craniotomy in the crus I or II area
of the mouse cerebellum was drilled leaving the dura mater intact; 100–600 nL
of virus solution (cell lysate or CsCl purified, 0.2 ?m filtered) was then slowly
injected (200–600 nL/h, ?0.03 bar) into the brain with a beveled quartz pipette
(5-?m tip opening) at an angle of 45° to the dura and to a depth of ?200 ?m.
Two-Photon Laser Scanning Microscopy. Imaging was performed with custom-
built 2-photon microscopes by using CfNT (Max Planck Institut for Medical Re-
search) and ScanImage (46) software. Bolus-loaded tissue was excited at 840 nm
by using a Mira 900 (Coherent Inc.) or MaiTai Ti:Sapphire laser (Spectra-Physics)
†Nimmerjahn A, Mukamel EA, Schnitzer MJ, Neuroscience 2008, November 15–19, 2008,
Washington, DC, abstr 337.2.
www.pnas.org?cgi?doi?10.1073?pnas.0809269106Hoogland et al.
focused into the tissue by using a 40?, 0.8 NA (Carl Zeiss or Olympus), or a 20?, Download full-text
0.95 NA water-immersion objective (Olympus). In tissue expressing
was done with the aid of custom-written LabView (National Instruments) soft-
1.8 mM CaCl2, 5 mM MgCl2, 5 mM Hepes?HCl, pH 7.3; filtered through a 0.2-?m
pore filter; and positioned in the cerebellar molecular layer. Alexa 594 (15 ?M)
by using a Pressure System IIe (Toohey Company). PPADS (500 ?M) and suramin
(1 mM; both drugs from Tocris) were applied directly to the brain surface.
Transgenic Animals. Transgenic mice expressing GFP under the glial fibrillary
acidic protein promoter [FVB/N-Tg(GFAPGFP)14Mes/J, stock no. 003257] were
obtained from Jackson Laboratories.
Analysis. Data were analyzed with custom-written programs in Matlab (Math-
works) and ImageJ (W. S. Rasband, ImageJ, National Institutes of Health, Be-
thesda, Maryland, http://rsb.info.nih.gov/ij/, 1997–2008).
To identify and quantify regions of spreading calcium change, for all movies
?F/F values were calculated for every pixel over the movie duration and thresh-
The ‘‘majority’’ morphological operation (MATLAB bwmorph) was applied to
each movie frame. This operation was repeated 3 times for all movie frames.
Additional mask editing was performed to remove noise that remained. To
detect glial waves, the sum A was taken of all ‘‘on’’ pixels in a movie frame. The
maximum value of A in a movie provided the maximal extent of a wave. Ellipses
were fit to the maximum extent of waves by using a stable direct least-square
fitting algorithm. Expansion time was defined as the time it took for a wave to
reach its maximum extent. Average duration of a wave was defined as the time
over which the mean fluorescence change reached 10% of the peak value or
for the wave to pass 2 points 10 ?m apart. Average wavefront velocity was
calculated by dividing the distance to maximal extent by the duration to maxi-
mum extent. A robust linear fit to the rising phase of the 2-dimensional area
Dapp, where Dapp? A/(4*t). Data in the text are presented as mean ? standard
deviation unless otherwise stated. Significance tests are one-tailed unless other-
ACKNOWLEDGMENTS. We thank Jonathan Charlesworth, Peggy Bisher, and
Hiroko Nakai for expert technical assistance and Ilker Ozden for helpful
comments and critical reading of the manuscript. This work was supported by
National Institutes of Health Grant NS045193, the National Science Founda-
tion, the W. M. Keck Foundation, the New Jersey Governor’s Council on
Autism, the Sutherland Cook fund (S.W.), and a Human Frontier Science
Project grant (F.H., J.N., and S.W.).
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