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Dynamic interactions ofcyclic AMP transientsand spontaneous Ca21 spikesYuliya V. Gorbunova*† & Nicholas C. Spitzer‡§

* Department of Physics, ‡ Neurobiology Section, § Center for Molecular Genetics,University of California San Diego, La Jolla, California 92093, USA† Present address: Department of Neuroscience and Cell Biology, University ofMedicine & Dentistry of New Jersey, 675 Hoes Lane, Piscataway, New Jersey08854, USA.............................................................................................................................................................................

Transient increases of intracellular Ca21 drive many cellularprocesses, ranging from membrane channel kinetics to transcrip-tional regulation1–5, and links of Ca21 to other second messengersshould activate signalling networks6–11. However, real-time kin-etic interactions have been difficult to investigate. Here we reportobservations of spontaneous increases in concentration of cyclicAMP (cAMP) in embryonic spinal neurons, and their dynamicinteractions with Ca21 oscillations. Blocking the production ofthese cAMP transients decreases the intrinsic frequency ofspontaneous Ca21 spikes, whereas inducing cAMP increasescauses spike frequency to increase. Transients of cAMP in turnare absent when Ca21 spikes are blocked, and are generated onlyin response to specific patterns of stimulated spikes that mimicendogenous Ca21 kinetics. We present a mathematical model ofCa21–cAMP reciprocity that generates the slow cAMP oscil-lations and reproduces the dynamics of Ca21–cAMP interactionsobserved experimentally. The model predicts that this module of

coupled second messengers is tuned to optimize production ofcAMP transients, and that simultaneous stimulation of Ca21 andcAMP systems produces distinct temporal patterns of oscillationsof both messengers. Our findings may prove useful in theinvestigation of the regulation of gene expression by second-messenger transients.

To investigate the interactions between Ca2þ and cAMP second-messenger systems we tested whether embryonic neurons generat-ing spontaneous Ca2þ spikes produce increases in the concentrationof cAMP. Transients of cAMP were observed at a frequency of4.3 ^ 1.1 h21 and duration of 2.9 ^ 0.3 min in 58% of youngneurons (n ¼ 17). Because the frequency of spontaneous Ca2þ

spikes decreases during development3, we also examined cAMPtransient generation in mature neurons. cAMP transients wereobserved in 50% of these cells, with a similar frequency(3.0 ^ 0.8 h21, P . 0.9) but longer duration (7.2 ^ 0.8 min,P , 0.001) than those of young neurons (n ¼ 12; Fig. 1, seeSupplementary Information for movie). cAMP increases occurredsynchronously throughout neurons, suggesting that they could bedriven by rapidly propagated Ca2þ spikes. The amplitudes of thesespontaneous cAMP transients were comparable to those of cAMPincreases induced by 50 mM forskolin, an activator of adenylylcyclase (AC), in both young and mature neurons.

We next determined whether changes in cAMP levels modulateCa2þ spike frequency. Sustained increases in cAMP produced byapplication of 50 mM forskolin increased the frequency of spon-taneous Ca2þ transients in 80% of young neurons from10.0 ^ 1.2 h21 to 26.5 ^ 1.4 h21 (n ¼ 15, P , 0.001; Fig. 2a). Inmature cells the effect was smaller, with a change in frequency from3.2 ^ 1.1 h21 to 5.2 ^ 1.5 h21 in 27% of cells (n ¼ 11, P , 0.03).Inhibiting AC with 40 mM dideoxyadenosine decreased the fre-quency of spontaneous Ca2þ transients in young neurons from10.7 ^ 1.8 h21 to 4.6 ^ 1.5 h21 in 80% of cells (n ¼ 10, P , 0.08;Fig. 2b, c), suggesting that endogenous AC activity regulates the

Figure 1 Spontaneous transient increases of cAMP in cultured spinal neurons. a, Surface

plot images illustrate increases and decreases in ratio fluorescence of FlCRhR in a

foreshortened view of a young neuron, from the soma (s) along the axon (a) to the growth

cone (gc). Colour scale indicates 520 nm/580 nm fluorescence ratio. Scale bar, 10 mm.

b, Digitized image intensities of the somata of two young neurons; forskolin applied

following the transients in the second provides a physiological calibration of the indicator.

c, As in b, for mature neurons.

Figure 2 Changes in cAMP levels modulate Ca2þ spike frequency. a, Sustained increase

of cAMP by stimulation with forskolin increases the frequency of Ca2þ spikes. b, Blockade

of spontaneous cAMP transients with dideoxyadenosine (Dd) reduces the frequency of

Ca2þ spikes. c, Histogram of Ca2þ spike frequency dependence on steady levels of cAMP

(n $ 5). d, Increases of cAMP induced with 5-s pulses of saline containing forskolin and

IBMX mimic naturally occurring transients. e, Phasic increase of cAMP (arrow) increases

the frequency of spontaneous Ca2þ spikes for a brief period. f, Histogram of Ca2þ spike

frequency before and after the cAMP pulse (n ¼ 7).

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natural spike frequency. Physiologically relevant imposition ofcAMP transients produced by 5-s pulses of a solution containing50 mM forskolin and 40 mM IBMX (3-isobutyl-1-methylxanthine, toblock phosphodiesterase, PDE), mimicking transients generatedspontaneously (Fig. 2d), increased Ca2þ spike frequency from12.0 ^ 1.4 h21 to 34.1 ^ 2.4 h21 for several minutes in 70% ofcells (n ¼ 10, P , 0.03; Fig. 2e, f). Increases of cAMP may act viaprotein kinase A (PKA). Consistent with this idea, blocking PKAwith 1 mM KT5720 reduced transient frequency to 4.4 ^ 1.7 h21 inyoung neurons (n ¼ 4 of 5 cells, P , 0.02; Fig. 2c).

Are Ca2þ spikes necessary to induce changes in cAMP levels?Elimination of naturally occurring Ca2þ spikes by the removal ofextracellular Ca2þ, or by the addition of Ca2þ and Naþ channelblockers in the presence of Ca2þ, blocked production of cAMPtransients (n ¼ 10), although responses to stimulation with for-skolin and IBMX demonstrated that AC remained active (n ¼ 3).We then asked whether there is an optimal pattern of Ca2þ spikes tostimulate cAMP transients. Ca2þ transients were generated indifferent patterns by depolarizing cells repetitively with briefpulses of 100 mM KCl in the presence of extracellular Ca2þ. Toreimpose more accurately the frequencies of Ca2þ spikes generatedspontaneously, we first applied wavelet analysis to recordings from12 young neurons to calculate the frequency composition. Thisalgorithm probes the local frequency content of the signals, incontrast to Fourier analysis that represents signals by harmonicoscillations extending over the whole time interval, and is lessvulnerable to local violations of signal regularity such as sharptransients, noise and shifts in baseline (see Methods and Sup-

plementary Information). All records exhibited three major fre-quencies. The low frequency (,4.3 h21) corresponds to theincidence of bursts and the highest frequency (,60 h21) to spikeswithin bursts, while the intermediate frequency (,8.2 h21) rep-resents single spikes (Fig. 3a).

No cAMP increases were observed following single Ca2þ transi-ents presented at 10 h21 (n ¼ 8; Fig. 3b, e). Triplets of Ca2þ

transients generated at 4 h21 with an intraburst frequency of60 h21 elicited cAMP increases in 60% of young neurons (n ¼ 5;Fig. 3c, f). Bursts of five Ca2þ transients produced at 2 h21 with anintraburst frequency of 60 h21 generated cAMP increases in 75% ofyoung neurons (n ¼ 4; Fig 3d, g). Although the total number ofspikes delivered within 1 h for each protocol was close to thespontaneous mean, the pattern of stimulation strongly influencedthe amplitude and duration of cAMP responses. Depolarizationalone was insufficient, because no cAMP increases were observedwhen Ca2þ was omitted from the saline and cells were depolarizedwith KCl (n ¼ 13). These observations suggest that specific patternsof Ca2þ spikes are selectively translated into cAMP transients,whereas other patterns are not.

To identify the constraints on the second-messenger interactionsnecessary to generate these experimental findings, we used a scheme(Fig. 4a) to construct a model producing intracellular Ca2þ oscil-lations and Ca2þ–cAMP interactions. To describe Ca2þ dynamicswe modified a single-compartment system12 in which [Ca2þ] isregulated by InsP3-receptor-activated stores and Ca2þ pumps,although a role for such stores has not yet been demonstrated inthe production of spikes in these neurons. The model is representedby the equations:

dx

dt¼ a1ðb 2 xÞ þa2x

ðb 2 xÞð1 2 yÞ

ðxþ b0Þ2 b1

x2

ðx2þa23Þ

þa4z2

ðz2þa25Þ

ð1Þ

dy

dt¼21yþ b2x2 ð1 2 yÞ

ðxþ b0Þð2Þ

where x and y represent the concentrations of Ca2þ and InsP3

receptor (InsP3R) bound to two Ca2þ; a i, b i and 1 are constants.The last term was added to equation (1) to account for positivefeedback on [Ca2þ] induced by increases in cAMP, consistent withPKA-driven phosphorylation of ryanodine and InsP3 receptors13,14.The dynamics of cAMP were described by a third equation (seebelow) in which cAMP is produced by Ca2þ-activated AC15 anddegraded by cAMP-activated PDE16. Differences in the kinetics ofcAMP generation and removal produce oscillations in response toCa2þ transients.

dz

dt¼ a1x4 2 a2

z3

ðz2þ a23Þ

ð3Þ

where z is the concentration of cAMP and a i are constants. Thestrength of feedback interactions and constants for the model werederived from experimental data (see Supplementary Information).

The model produces spontaneous patterns of Ca2þ and cAMPoscillations similar to those observed experimentally. First, cAMPtransients are generated by Ca2þ increases and terminated by self-activated inhibition (Fig. 4b, top and bottom). Although thetransients produced by the simulation are periodic, introductionof noise would generate aperiodic behaviour resembling exper-imental records17. Second, wavelet analysis of Ca2þ transientsproduced by the model shows strong periodic wavelet coefficientsat scales of 80 and 15, identifying dominant frequencies similar tothose from analysis of experimental records (Fig. 4b, middle).Third, transient increases of cAMP increase the frequency of Ca2þ

transients briefly (Fig. 4c). Fourth, Ca2þ spikes imposed in differentpatterns are differentially effective in stimulating increases of cAMP

A A A A A A B B C

B CA

Figure 3 cAMP transients decode specific patterns of Ca2þ spikes. a, Wavelet analysis

identifies prominently represented frequencies of spontaneous Ca2þ spikes. Top,

digitized record of Ca2þ indicator fluorescence from young neuron imaged for 1 h.

Bottom, pseudocolour density plot of the wavelet coefficient, Cab, as a function of the

scale, b, and time (as for the top panel) for this record. Yellow horizontal lines indicate

strong periodic Cab values at specific scales (180, 80 and 12) corresponding to

frequencies at which spikes are generated. b–d, Different patterns of stimulated Ca2þ

spikes. A, single spikes; B, three spikes; C, five spikes. e–g, cAMP responses to these

patterns of Ca2þ spike stimulation; red arrows mark the times of imposition of the patterns

of Ca2þ transients indicated by the letter above each one.

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(Fig. 4d). Selective increase of cAMP by distinct patterns of Ca2þ

transients appears to result from the match of AC and PDE kinetics

with the timescale of Ca2þ oscillations. Elimination of any one of

the three feedback loops (Fig. 4a) abolishes or dramatically alters the

patterns of transients generated by the model (data not shown).

Model simulations make several experimentally testable predic-

tions. In particular, the model predicts that there is an optimal

pattern of Ca2þ transients for eliciting increases of cAMP. Wedetermined the cAMP response, defined as the ratio of signalamplitude (mM) to signal duration (s), as a function of intraburstCa2þ spike frequency and Ca2þ spike burst duration (Fig. 4e).Contours in the x–y plane indicate combinations of spike number/burst and intraburst frequency yielding equivalent cAMP responses.Because the number of spikes within a burst that elicits themaximum response corresponds to that identified in experimentalrecords, the biological system appears to be tuned to its optimumperformance; the triplet maximum arises from the dynamics ofactivation of AC and PDE. The model also predicts the result ofcoincident changes in Ca2þ and cAMP metabolism. Simulationsaltering [InsP3] and AC activity simultaneously reveal conditionsproducing distinct linkages of Ca2þ and cAMP transients (Fig. 4f).These changes in their dynamical patterns make possible differentialactivation of kinases and gene expression.

Hormones, growth factors, and drugs elicit cellular responses inthe form of Ca2þ oscillations, the frequencies of which are deter-mined by the amount and type of the agent18–21. Patterns ofspontaneous and stimulated Ca2þ transients drive transcription ofspecific genes22–24, and stimulated cAMP transients also regulategene expression25,26. We have shown that only certain bursts of Ca2þ

spikes generate a cAMP increase. Our results may be useful inunderstanding the coding of gene expression by interactionsbetween Ca2þ transients and cAMP oscillations. Higher frequenciesof Ca2þ spikes have been shown to control gene expression moredirectly via Ca2þ-dependent kinases that are not efficiently activatedby low frequencies of Ca2þ transients. For example, cAMP increasesinduced by serotonin at frequencies similar to those reportedhere lead to translocation of PKA catalytic subunits into the nucleusof Aplysia neurons and gene expression underlying long-termfacilitation25,27,28. The theoretical model combining Ca2þ oscillatorymachinery and feedback regulation of cAMP synthesis predicts theexistence of these low-frequency cAMP transients rather than high-frequency events29. These results suggest that it could be fruitful toinvestigate interactions among other classes of second messengers30,as tiers of messenger systems may be necessary to generate differentpatterns of transients that produce unique cellular responses tostimulation. A

MethodsCell cultureSpinal neurons from neural plate stage Xenopus embryos were cultured3 and allowed todevelop for 8–12 h (young neurons) or 18–24 h (mature neurons). During imagingexperiments, cells were usually superfused at a rate of 5 ml min21 with saline containing2 mM Ca2þ. Ca2þ spikes were blocked by substitution with a Ca2þ-free mediumcontaining 1 mM EGTA or by addition of a mixture containing 1 mM GVIA q-conotoxin(Alomone), 0.02 mM calcicludine (Calbiochem), 1 mM flunarizine and 1 mg ml21

tetrodotoxin (Sigma). Ca2þ spikes were stimulated by 5-s pulses of saline containing100 mM KCl (ref. 3).

ImagingIntracellular Ca2þ was measured using Fluo-4 AM (Molecular Probes). Cells wereincubated in 5 mM indicator for 40 min and washed. Intracellular cAMP was measuredusing FlCRhR (Molecular Probes; average stock concentration ,20 mM) injected intosingle cell somas in 1 mM Ca2þ medium with a microinjector system (Eppendorf).Injection pressure was ,170 hPa and capillary holding pressure was ,130 hPa. Neuronswere imaged with a BioRad MRC-1024 confocal imaging system with a 15-mW Kr/Ar ionlaser and an Olympus microscope with 60£objective (NA 0.9). At 1–3% of full power, thelaser provided excitation at 488 nm wavelength, suitable for both dyes. The Fluo-4emission filter had a bandpass of 535/22 nm and those of the FlCRhR emission filters were540/30 nm and 580/32 nm. For cAMP measurements two single-wavelength emissionimages were simultaneously acquired every 10 s; changes in fluorescence were observed for.20 min in response to sustained application of 50 mM forskolin. For Ca2þ imaging therate of acquisition was 0.2 Hz.

Data analysisFluo-4 fluorescence was analysed with NIH Image (W. Rasband). Changes were assessedby average pixel intensity within cell bodies. Only fluorescence increases above 150% ofbaseline were scored as spikes. For analysis of FlCRhR fluorescence, traces were correctedfor photobleaching, background was subtracted and the ratio of 520/580 nm emission wascalculated. At low laser power, no autofluorescence was detected. Cells were studied only if

Figure 4 Modelling dynamics of Ca2þ–cAMP interactions. a, Scheme illustrating the

interactions on which the model is based. InsP3, inositol trisphosphate; InsP3R, InsP3

receptor. b, Top and bottom, simulated spontaneous Ca2þ and cAMP oscillations.

Baseline [Ca2þ] and [cAMP] are ,20 and ,200 nM. Middle, wavelet analysis of

modelled Ca2þ oscillations. Nomenclature as in Fig. 3a. c, Simulated transient increase of

cAMP increases the frequency of Ca2þ spikes transiently. d, Different patterns of

simulated Ca2þ spikes are selectively potent in eliciting cAMP responses. e, Variation of

spike number (proportional to burst duration) and intraburst spike frequency identifies a

maximum for the cAMP response, defined as the ratio of signal amplitude (mM, baseline to

peak) to the signal duration (s, baseline to baseline) to provide a measure of sharpness, for

triplets of spikes over a range of intraburst frequencies. f, Simultaneous increases in

[InsP3] and AC activity (a1 in equation (3)) within physiological ranges predict (1) a realm in

which the complex pattern of Ca2þ and cAMP dynamics (b) results (red), (2) a domain in

which cAMP oscillations are locked to Ca2þ oscillations one-to-one (yellow), and (3) a

region in which no Ca2þ or cAMP oscillations occur (blue).

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they responded to forskolin stimulation, and cAMP transients were scored only if 520- and580-nm traces changed in opposite directions. Statistical analysis was performed using theKolmogorov–Smirnov non-parametric test; values are presented as mean ^ s.e.m. andwere considered significantly different for P , 0.05.

ComputationConstants in the model are annotated in Supplementary Information; MATLAB 6.0(Mathworks) was used for numerical calculations. Wavelet analysis was performed usingthe Morlet wavelet from the standard numerical ‘wavelet analysis’ package (Mathworks).Wavelet analysis produces a set of coefficients, C ab, calculated using the formulaCab <

Ðdt f ðtÞW½ðt 2 aÞ=b�; where W is the analysing function referred to as the ‘wavelet’,

a represents time localization and b is the scale, which is inversely proportional to the localfrequency. To avoid edge effects, only the central 40 min of each hour were considered. Noperiodic structure was evident when this method was tested with white noise.

Received 28 December 2001; accepted 22 April 2002; doi:10.1038/nature00835.

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Supplementary Information accompanies the paper on Nature’s website

(http://www.nature.com/nature).

AcknowledgementsWe thank S. R. Adams, T. M. Gomez, I. Hsieh and N. Lautermilch for assistance,

A. Rozhkov for advice on modeling, and P. H. Diamond, M. B. Feller and T. M. Gomez forcomments on the manuscript. This work was supported by a Burroughs-Wellcome LJISfellowship (Y.V.G.) and NIH NINDS grant (N.C.S.).

Competing interests statement

The authors declare that they have no competing financial interests.

Correspondence and requests for materials should be addressed to N.C.S.

(e-mail: nspitzer@ucsd.edu).

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Determination of left–right patterningof the mouse embryo by artificialnodal flowShigenori Nonaka, Hidetaka Shiratori, Yukio Saijoh & Hiroshi Hamada

Graduate School of Frontier Biosciences, Osaka University, 1–3 Yamada-oka,Suita, Osaka 565-0871, Japan; and CREST, Japan Science and TechnologyCorporation (JST), Japan.............................................................................................................................................................................

Substantial insight has recently been achieved into the mechan-isms responsible for the generation of left–right (L–R) asymme-try in the vertebrate body plan1–4. However, the mechanism thatunderlies the initial breaking of symmetry has remained unclear.In the mouse, a leftward fluid flow on the ventral side of the nodecaused by the vortical motion of cilia (referred to as nodal flow) isimplicated in symmetry breaking5, but direct evidence for therole of this flow has been lacking. Here we describe the develop-ment of a system in which mouse embryos are cultured under anartificial fluid flow and with which we have examined how flowaffects L–R patterning. An artificial rightward flow that wassufficiently rapid to reverse the intrinsic leftward nodal flowresulted in reversal of situs in wild-type embryos. The artificialflow was also able to direct the situs of mutant mouse embryoswith immotile cilia. These results provide the first direct evidencefor the role of mechanical fluid flow in L–R patterning.

The breaking of symmetry during vertebrate development isthought to occur in or near the node. In the mouse embryo, theventral surface of the node (nodal pit) possesses several hundredmonocilia6 that rotate in a clockwise direction, and this rotationalmovement somehow generates a leftward laminar flow5. The lack ofthis nodal flow as a result of impaired ciliary development leads torandomization of body situs5,7–10. Nodal flow has thus been pro-posed to trigger a signalling cascade responsible for L–R patterningby transporting an unidentified molecule towards the left side of thebody. However, this ‘nodal flow hypothesis’ has remainedunproved. It raises many questions, the most important of whichis whether the nodal flow is a genuine symmetry-breaking event orsimply a manifestation of such an event.

One approach to test directly the role of nodal flow would be tomanipulate the flow mechanically and to examine how such manipu-lation affects L–R patterning. To achieve this goal, we developed aculture system (flow culture) in which embryos are allowed todevelop under a constant flow of culture medium driven by aperistaltic pump (Fig. 1a). In this system, octopus-trap-like potshold embryos in their proximal region (Fig. 1b, c), so that the distalregion, including the node, is exposed to the flow. The artificial flowcan be controlled in two ways: First, the flow can be leftward (Fig.1b) or rightward (Fig. 1c) with respect to the L–R axis of theembryo, depending on how the embryos are placed in the pots.Second, the rate of the flow can be adjusted to either fast or slow.

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