michael r. guevara et al- phase resetting of spontaneously beating embryonic ventricular heart cell...

8/3/2019 Michael R. Guevara et al- Phase resetting of spontaneously beating embryonic ventricular heart cell aggregates

1/8

Phase resetting of spontaneously beating embryonicventricular heart cell aggregates

MICHAEL R. GUEVARA, ALVIN SHRIER, AND LEON GLASSDepartment of Physiology, McGill University, Montreal, QuebecH3G 1 Y6, Canada

GUEVARA,MICHAEL R., ALVIN SHRIER, AND LEON GLASS.Phase resetting of spontaneously beating embryonic ventricularheart cell aggregates. Am. J. Physiol. 251 (Heart Circ. Physiol.20): Hl298-Hl305, 1986.-The influence of isolated 20-msduration current pulseson the spontaneous hythm of embry-onic chick ventricular heart cell aggregateswasstudied.A pulsecould either delay or advance he time of occurrenceof the nextaction potential, dependingon whether it fell early or late inthe cycle. As the stimulus amplitude was increased, he tran-sition from delay to advanceoccurred over a narrower range ofcoupling intervals. At low-stimulus amplitudes the transitionfrom delay to advanceoccurred n a smoothcontinuous fashion;at medium-stimulusamplitudes the transition was discontin-uous;at high-stimulusamplitudesgradedaction potentials wereseen. It was impossible o annihilate spontaneousactivity inaggregates ith a singlestimulus.The phase-resetting esponseto hyperpolarizing pulseswas qualitatively the reverse of thatproducedby depolarizing pulses.A very high-amplitude depo-larizing or hyperpolarizing pulsecould produce rapid repetitiveactivity. Theoretical aspectsof thesephenomenaare discussed.all-or-none depolarization; graded action potentials; annihila-tion; embryonic chick

DELIVERY OF A SINGLE premature stimulus to the heartcan result in dramatic changes in its rhythmic activity.An appropriately timed stimulus delivered to a normalhealthy heart can abolish rhythmicity by inducing fibril-latory activity. In isolated cardiac tissue a single prema-ture stimulus can annihilate spontaneous activity (14,20, 21) and can also terminate as well as start triggeredactivity (10). However, the effect of a premature stimulusis usually not quite so drastic; generally, there is aresetting of the cardiac rhythm.Several recent studies have analyzed the phase reset-ting of cardiac tissue by brief depolarizing and hyperpo-larizing inputs. The magnitude of the phase resettingobtained depends on the phase in the cycle at which acurrent pulse is injected as well as its polarity, amplitude,and duration (8, 15, 17, 19-23, 27-30). For example, inresponse to a brief depolarizing input there is a delay tothe next action potential if the pulse is delivered early inthe cardiac cycle and an advance if the stimulus isdelivered late in the cycle. The transition from delay toadvance occurs over an increasingly narrow range ofstimulus phase as stimulus amplitude increases. Theresponse to a single stimulus delivered at various phasesin the cycle can be used to predict the effect of periodi-cally delivered stimuli (15, 17, 19, 22, 23, 27, 31).

In this paper we describe the effects of single stimulion the spontaneous rhythm in aggregates of ventricularcells from embryonic chick heart. In this virtually iso-potential preparation (7, 12, 13, 24), propagation effectsare minimized. This facilitates interpretation and mod-eling of the data. We pay particular -attention to phase-resetting behavior where transition from delay to ad-vance is a sensitive function of stimulation parameters.These transitioncharacterized in .a1 regionprevious .s have not been adequatelywork. In some preparations,delivery of a single stimulus can lead to a long delay asa result of several skipped beats; in others, there is atransient acceleration of the cardiac rate. We discusstheoreticalnomena. mechan sms underlying some of these phe-

MATERIALS AND METHODSTissue culture. Aggregates were prepared followingtechniques of DeHaan and Fozzard (13) as previouslydescribed (9). White Leghorn chick embryos were incu-bated for seven days at a temperature of 37C and arelative humidity of 85%. The embryos were decapitated,and the

isolated,apical portionsfragmented, and

of the heart ventriclesdissociated into single

werecells.Dissociation was carried out by a multiple-cycle proce-dure in an enzyme-containing solution (11). The cellsuspension was filtered through a membrane with a 12.O-pm-diameter pore size and centrifuged at about 170 g for15 min. The cells were resuspended, counted, and ali-quoted into 25-ml Erlenmeyer flasks each containing 3ml of maintenance medium at a density of 5 x lo5 to 7

x lo5 cells per flask. The flasks were gassed with amixture of 5% C02-10% Oz-85% N2, sealedwith a siliconerubber stopper, and placed on a gyratory table (70 rev/min) for 48-96 h at 37C to allow spheroidal aggregatesto form.The dissociation medium consisted of 5.25 X 10B5g/ml crystalline lyophilized trypsin (Worthington Bio-chemical, 245 U/mg) and 5 X 10m6 /ml deoxyribonucle-ase I (Worthington, 9.1 X lo4 U/mg) in a Ca2+-Mg2+-free, phosphate-buffered balanced salt solution with con-centrations (mM) as follows: NaCl 116.0, KC1 5.4,NaH2P04 0.44, Na2HP04 0.95, dextrose 5.6. The pH ofthe dissociation medium was adjusted to 7.3 with either1 N HCl or 1 N NaOH.The maintenance medium, a modification of medium818A (l3), consisted of 2% horse serum (Kansas CityBiological), 4% fetal bovine serum [Grand Island Biolog-H1298 0363-6135/86 $1.50 Copyright0 1986 the AmericanPhysiologicalociety


2/8

PHASE RESETTING OF EMBRYONIC HEART-CELL AGGREGATES H1299ical (GIBCO)], and 20% medium 199 (GIBCO) in abicarbonate-buffered balanced salt solution. The finalconcentrations (mM) were approximately as follows:NaCl 116.0, KC1 1.3, CaC12 1.8, MgS04 0.8, NaH2P040.9, NaHC03 20.0, dextrose 5.5. The antibiotic gentami-tin sulfate (Schering, Garamycin, 10 mg/ml) was addedto the medium to yield a final concentration of 5 X low5g/ml.The enzyme-inactivating medium was the same as themaintenance medium but with the following exceptions:0% fetal bovine serum, 10% horse serum, and -4 mMKCl. All solutions were filtered with a sterile filter havinga 0.45@m-diameter pore size.Electrophysiology. After 2-4 days of gyration culture,the reaggregates of cardiac cells were poured into a 35 Xlo-mm plastic tissue culture dish (Falcon 3001). Mineraloil was layered out on top of the medium to preventevaporation. The medium was gassed from above by atoroidal gassing ring at a flow rate of 200 ml/min with agas mixture of 5% C02-10% 0$35% N2 (13). The bicar-bonate buffer in the medium maintained the pH at -7.2-7.3. Temperature was maintained at 36 + 1C. Phenolred in the maintenance medium (0.04 mg/ml) provideda rough continuous estimate of the pH. Under theseconditions, >98% of the aggregates in a dish beat spon-taneously. Mean aggregate diameter, taken to be themean of the minor and major axes in the horizontalplane, could be estimated accurately and repeatedly towithin one-half of a minor division of the graticule (i.e.,to +19 pm).Electrical activity was recorded intracellularly usingmicroelectrodes filled with 3 M KC1 (electrode resistance20-100 MQ). Transmembrane potential was registeredusing an amplifier with negative capacitance compensa-tion. The bathing medium was maintained at virtualground by being coupled to a current-to-voltage converter(lo-100 mV/nA) through an agar-salt bridge and a chlo-rided silver wire. Pulses of current were injected into theaggregate through the same microelectrode used for re-cording the membrane voltage and their amplitudes mea-sured by the current-to-voltage converter. Currents weremeasured to the nearest 0.5 nA. Two programmablestimulators (Frederich Haer, Pulsars 4i and 6i) connectedto external logic circuitry were used.Voltage and injected current waveforms were moni-tored on a digital oscilloscope (Nicolet model 206) andrecorded on an FM instrumentation recorder at a tapespeed of 33~ in/s (Hewlett-Packard model 3964A; 3-dBfrequency response at 33/4 in./s: DC-1250 Hz) for lateroff-line analysis.The protocol involved a 20-ms duration current pulsedelivered at various coupling intervals after every 10spontaneous beats. The coupling interval was automati-cally incremented (by a multiple of 1 or 10 ms) scanninga part of or, in some cases, the entire spontaneous cycle.The above protocol was then repeated for a differentcurrent amplitude, duration, or polarity.Data analysis. Off-line analysis was carried out withthe digital oscilloscope and by an automated system.Magnetic tapes were played back at a tape speed of 15/16 in./s (i.e., l/4 real time), low-pass filtered, and the

voltage waveform then sampled at 250 Hz by a Z80-basedmicroprocessor system (Cromenco System III fitted witha California Data, AD-100 12bit analog-to-digital con-verter). The digitized waveform was transferred over anRS-232 serial line at 9,600 baud to a minicomputer(Hewlett-Packard model HP1000 series F) and stored ondigital magnetic tape. Interbeat intervals were extractedout of the digitized waveform by a pattern recognitionprogram.All of the experimental voltage traces in this report(with the exception of Fig. 1A) were obtained by playingback the tape-recorded signal to the digital oscilloscopethrough a low-pass filter (to avoid aliasing). The contentsof the oscilloscope memory were then reconverted to ananalog signal and sent to an analog X-Y plotter (Hewlett-Packard model 7015B).RESULTS

Spontaneous activity of the aggregate. Heart cell aggre-gates generally beat with a regular rhythm (Fig. 1, A and

# 11 setB 750

F

600 +- -- -- --

i 825

C

IBli+l(msec)

(msec)FIG. 1. A: tracing of transmembrane voltage recorded during spon-taneous unperturbed act ivi ty in an aggregate illustrating regularity ofbeating. Unlike voltage tracings in other figures in this paper, thistracing was obtained by sending output of tape recorder directly toplotter. To p and bottom of vertical calibration bar in this and allsubsequent figures indicate 0 mV and -50 mV, respective ly. (Aggregateno. 1: diameter = 114 pm.) B: interbeat interval (IBI,) plotted vs .interval number (i) from a period of unperturbed act ivi ty. No. of beats= 826. Precision in measuring an interbeat interval is +l.O ms. Mean,SD, and coefficient of variation were 686 ms, 10.2 ms, and 0.015,respectively . C : scattergram of same data shown in B with each of 824interbeat intervals plotted as function of immediately preceding inter-beat interval. Straight line plotted through the data is least-squares f itto data; it has slope o f 0.92 and coeff icient of determination (r) of0.922. (Aggregate no. 2: diameter = 105 pm).


3/8

H1300 PHASE RESETTING OF EMBRYONIC HEART-CELL AGGREGATESB), with a coefficient of variation (SD/mean) of the(electrical) interbeat interval of -0.02 (see also Ref. 7).We define the (electrical) interbeat interval to be thetime from the crossing of 0 mV on the upstroke of oneaction potential to the zero crossing on the upstroke ofthe following action potential. In most aggregates, thereis occasional bursting behavior, during which the beatrate of the aggregate transiently increases (17). Duringspontaneous activity, the interbeat interval of any cycleis highly correlated with that of the immediately preced-ing cycle (Fig. 1C).Response to stimulation with a single depolarizing cur-rent pulse. Data were obtained at only one depolarizingamplitude in 10 aggregates and at two or more amplitudesin another 17 aggregates: these 27 aggregates were takenfrom 21 cultures. The mean diameters of these aggregateswere in the range of 90-225 pm, and the intrinsic inter-beat intervals after impalement were in the range of 450-1,200 ms. Figure 2A shows the effect of injecting a singledepolarizing current pulse of amplitude 10 nA and du-ration 20 ms into a spontaneously beating aggregate. Thecontrol interbeat interval (7& the perturbed interval(Tl), and the interbeat interval of the first poststimuluscycle (7& are indicated. The coupling interval (t,) isdefined to be the time from the zero crossing on theupstroke of the action potential immediately precedingthe stimulus to the beginning of the stimulus. The phase4 of the stimulus is 4 = tc/To (0 G 4 < 1). Activity intwo widely separated cells in an aggregate is virtuallysynchronous, even after delivery of a stimulus (compareupper and lower traces in Fig. 2A). The time differencebetween zero crossings of all pairs of upstrokes recorded(Fig. 2) with electrodes -120 pm apart is at most 50 ps,which agrees with previous measurements in heart-cellaggregates during spontaneous activity ( 13).Figure 2, B and C, shows the effect o f delivering adepolarizing pulse of 20-ms duration at a coupling inter-val that is systematically incremented in lo-ms steps; inFig. 2B the stimulus current amplitude is low (6.5 nA)and in Fig. 2C it is high (24 nA). At the high-stimulusamplitude graded action potentials are produced (Fig.20The normalized perturbed interbeat interval T1/To isplotted as a function of 4 in Fig. 3 for various stimulusstrengths. The progression in the data from Fig. 3Athrough Fig. 3F is typical of the changes in T,/To seenin any one aggregate as the stimulus amplitude is in-creased. Since the stimulus artifact obscures the actionpotential upstroke when the stimulus is delivered lateenough in the cycle to be a threshold stimulus, T, canonly be estimated to within one-half of the pulse durationin such instances. Also, when graded action potentialsappear, one must arbitrarily decide on what is to becalled an action potential. For example, we would callthe event after the stimulus at t, = 120 ms in Fig. 2C anaction potential but not the one after the stimulus at tc= 110ms. Also note that beyond a certain point, increaseof the stimulus amplitude produces no significant changein the data; the response appears to saturate (cf. Fig. 3Ewith Fig. 3F).The main features of Fig. 3 are that 1) a stimulus of a

238

B -Ju cAJk16OJq ; 9&J 1) or advancing (i.e., T1/TO < 1) the time of occurrenceof the next action potential depending on the phase inthe cycle at which it is delivered; 2) the coupling intervalat which the transition from delay to advance occursmoves to a smaller value as the stimulus amplitude isincreased; 3) the transition from maximal prolongation(i.e., T1/TO a maximum) to maximal abbreviation (i.e.,T,/T, a minimum) of cycle length takes place over anincreasingly narrow range of the coupling interval as thestimulus amplitude is increased.


4/8

PHASE RESETTING OF EMBRYONIC HEART-CELL AGGREGATES H1301

IO08

Tn,0604

I 2

I 0

08

06

04

0 02 04 06 08 IO 0 02 04 06 08 lo+ #

FIG. 3. Data points from phase-resetting runs carried out at 6different stimulus amplitudes in one aggregate (same aggregate as inFig. 2, B and C). Normalized perturbed cyc le length ( 7JT0) is plottedvs . the normalized coupling interval (4 = tc/TO). Crosses are placedmidway through stimulus -artifact which obscures action potentialupstroke. SoLid lines are extrapolations based on results obtained inother aggregates and correspond to membrane reaching threshold dur-ing stimulus. Data points are found along dashed lines in A-C whenphase-resetting run is repeated. (Aggregate no. 1: diameter = 114 pm.)In addition to the striking effect on the timing of theonset of the firs t action potential after a stimulus, thereare other less marked effects on the durations of the

poststimulus and subsequent cycles. A cycle that isshortened by a depolarizing stimulus falling late enoughin its cycle tends to be followed by a poststimulus cyclethat is longer than the control cycle, whereas a cycle thatis prolonged by an early stimulus tends to be followed bya poststimulus cycle that is briefer than control (Fig.2A). At lower stimulus amplitudes (producing responsessuch as those shown in Fig. 2B), for a prolongation of-20% (i.e., T1/TO = 1.2) the poststimulus cycle is typi-cally shortened by -24% (i.e., T,/T, N 0.950.98),whereas for an abbreviation of -50% (i.e., 7JT0 E 0.5),the poststimulus cycle is typically lengthened to 7JT0 s1.02-1.05.Discontinuitv in the whase-resetting reswonse:

a&or-none depolarization. As stimulus amplitude is in-creased, the transition from prolongation of cycle lengthto abbreviation of cycle length occurs over an increas-ingly narrow range of the coupling interval. Indeed, inthe aggregate of Fig. 3, at a stimulus amplitude of 8 nA,the transition from maximal prolongation to maximalabbreviation of cycle length occurs with a change in tc of10 ms. However, the transition is not discontinuous,since intermediate values of 7JT0 were found on re-peated stimulation with tc in the transitional range ofcoupling intervals (i.e., with t, = 160 or 170 ms).At a somewhat higher current than that necessary toobtain this continuous response, but at a current lowerthan that needed to obtain graded action potentials (Fig.2C), the transition from maximal prolongation to abbre-viation occurs much more abruptly. To probe this phe-nomenon in more detail, we investigated the effect ofchanging tc in 1-ms increments in the range of stimulusamplitude and timing that produces the abrupt transitionin another aggregate. The coupling interval at which thisrapid transition occurs is always just a bit less than theaction potential duration. Figure 4A shows one example,where a stimulus was delivered 11 times at a fixed cou-pling interval of 142 ms. Two types of responses occurred:one at a lengthened interbeat interval (3/ll trials) and

A

B141

Jl /

142

143I I1 set

FIG. 4. A: superimposed tracings from 11 repeated trials with a 27-nA amplitude, 20-ms duration current pulse at a fixed coupling interval( tc) of 142 ms. Eight of these trials produced an advance in time ofoccurrence of next beat, whereas other 3 produced a delay. Unperturbedinterbeat interval of this aggregate was -462 ms. Thus discontinuityin the response T l is ~0.83 of spontaneous cycle length. B: 5/5 trialsattempted at tc = 141 ms produced only delays (Tl = 565 ms), whereas717 at tc = 143 ms produced only advances (T, = 153 ms). 3/l1 trialsat tc = 142 ms produced advances, the other 8 produced delays.(Aggregate no. 10: diameter = 149 urn.)


5/8

Hl302 PHASE RESETTING OF EMBRYONIC HEART-CELL AGGREGATESthe other at a shortened interbeat interval (8/11 trials).Responses with intermediate values of T,/T , were notobserved. In addition , the variability in TI at fixed tc seenat slight ly lower stimulus amplitudes did not occur. At tc= 141 ms only prolongation of the cycle length wasobserved (5 trials), whereas at t, = 143 ms only shorten-ing was observed (7 trials) (Fig. 4B). In experiments onother aggregates in which as many as 50 trials at a fixedcoupling interval were carried out, a similar dichotomyin the response was observed. This threshold-like behav-ior may be called all-or-none depolarization.The abrupt transition shown in Fig. 4 was seen in al laggregates in which t, was changed in I-ms increments.The current amplitude at which it is seen varies fromaggregate to aggregate, since the electrophysiologicalproperties of aggregates can differ, even if they are ofcomparable size (9,13). However, in al l aggregates whereboth all-or-none depolarization and graded action poten-tials were seen, all-or-none depolarization occurred at aleve l just below that a t which graded action potentialsmade their appearance.Skipped beats. In 24 aggregates, al l of which had in-trinsic periods of I s (only 3 preparations studied had such long interbeatintervals), much larger maximal prolongations could beobtained. These long delays were usually associated withsubthreshold oscillatory activity in the pacemaker rangeof potentials (Fig. 5) and were only produced within anarrow range of coupling i ntervals; increase or decreasein t, by as little as 10 ms usually destroyed the effect.The response is variable in that the long prolongation isoften of a different length and might be seen at a slightlydifferent coupling interval when the phase-resetting runis repeated keeping the stimulus amplitude and durationfixed. Indeed, there can be significant fluctuation in theresponse when repeated trials at a fixed coupl ing intervalare carried out; threshold is attained at one or other ofthe peaks of the subthreshold oscil lation (Fig. 5, A andB). The longest prolongation observed in this aggregatewas TI/TO = 5.3 (Fig. 5B: tC = 620 ms).Careful attempts to annih ilate spontaneous activity inthe aggregate using a single ZO-ms duration depolarizingpulse were made by systematically varying the stimulustiming and amplitude as described above. In no case wasit possible to annih ilate spontaneous activity.Response to stimulation with a single hyperpolar izingcurrent pulse. The response to a hyperpolarizing pulsehas also been studied in nine aggregates. We summarizethe results (further details can be found in Ref. 17): 1)the response to a hyperpolarizing current pulse is thereverse of that produced by a depolarizing pulse, in thata stimulus fall ing early in the cycle produces an abbre-viat ion of cycle length, whereas one fal ling later producesa prolongation of cycle length; 2) the transition frommaximal prolongation of cycle length to maximal abbre-viat ion of cycle length becomes more abrupt as thestimulus amplitude is increased, until it eventually be-comes effectively discontinuous. An apparent disconti-nuity occurs at a small value of t,, when the stimulus

A

570

B600

570

a b

\620

FI G. 5. A: 10 repeated trials at fixed c oupling interval (tC) of 570 ms.Pulse amplitude was 9 nA and pulse duration 20 ms. Threshold isattained either at first crest of subthreshold oscillatory activity (groupof 7 action potentials labeled a) or at the second crest (group of 3 actionpotentials labeled b). B: 3 trials from a phase-resetting run in whichthe coupling interval was changed in lo-ms steps. Pulse amplitude was6.5 nA, pulse duration 20 ms. Action potential after delivery of stimulusfires on first (tC = 600 ms), second ( tC = 570 ms), or third ( tC = 260 ms)crest of subthreshold oscillatio n in membrane voltage. (Aggregate no.8: diameter = 170 pm.)

falls during the plateau of the action potential (all-or-none repolarization); and 3) a high-amplitude stimuluscan produce graded action potentials, sometimes via ananodal-break effect.Pulse-induced rapid repetitive activity. Rapid repetitiveactivity in response to a high-amplitude depolarizingcurrent pulse was a rare phenomenon seen in only twoaggregates from two different cultures. Figure 6A


6/8

PHASE RESETTING OF EMBRYONIC HEART-CELL AGGREGATES H1303

1 setFI G. 6. Rapid repetitive activity induced by a single 20-ms duration

current pulse, A: depolarizing pulse of amplitude greater than 100 n4with coup ling interval (t,) = 130 ms. Exact current is not known dueto saturation of current measurement circuitry. Rapid activity was notseen at a current amplitude estimated to be about two-thirds of thisamplitude: only a single extrasystole occurred. (Aggregate no. 13: di-ameter = 190 pm.) B: hyperpolarizing pulse of amplitude 37 nA, withL = 8 ms. Action p otential upstroke and stimulu s artifact retouched.(Aggregate no. 11: diameter = 132 pm.)aggregates in which this phenomenon was seen came-from cultures in which aggregates appeared to be con-tracting normally under the microscope and which hadthe usual high percentage of spontaneously beating ag-gregates. Furthermore, the action potential parametersmeasured from the aggregates in which the rapid repeti-tive activity was seen were within the usual range.In contrast to the case of a depolarizing stimulus, rapidrepetitive activity was often seen in response to a high-amplitude hyperpolarizing stimulus (e.g., Fig. 6B). Also,in contrast to the case of a depolarizing stimulus, theeffect was strongly phase dependent, in that rapid repet-itive activity could only be provoked by a stimulus fallingvery early in the cycle (e.g., Fig. 6B). In addition, therewere marked decreases in the absolute values of themaximum diastolic potential and of the overshoot poten-tial for several beats after injection of the stimulus (Fig.W .DISCUSSION

A large number of studies have demonstrated a bi-phasic Gsponse of spontaneously beating cardiac tissueto a single stimulus. This includes experiments on heartcell aggregates (8, 13, 15, 17, 19, 28, 29) and isolatedcardiac tissue (14, 20-23, 27, 30) as well as clinical datafrom patients with parasystole (4). A similar responsehas been found theoretically in ionic models (2, 3, 8), inelectronic models (26), and in simple two-dimensionallimit-cycle oscillations (18, 28, 31).Over an intermediate range of stimulus amplitudes, inresponse to a depolarizing current pulse, there is anabrupt transition from lengthening to shortening of theperturbed cycle length (Fig. 4). There are fundamentalnroblems in ascertaining whether or not the normalizedperturbed cycle length ?P,/T, is truly a discontinuousfunction of the normalized coupling interval tJTO (16,17). In Fig. 4A an abrupt transition of the cycle lengthcan be seen without any evidence, even after many trials,of intermediate responses.Investigation of the response of an ionic model of theaggregate to perturbation with a depolarizing current-pulse -suggestsfundamentally that, at lower stimulus amplitudes, T, isa conti nuous function of the coupling

interval tc (8). Although the response is continuous, thetransition from prolongation to abbreviation of the cyclelength can be very steep. For example, in the ionic modelof a 15O-pm-diameter aggregate, for a current pulse am-plitude of 16.9 nA, an increment in the coupling intervalof as little as 10 pusmust be used to demonstrate theunderlying continuity (Ref. 8, Fig. 3B). At double thisamplitude, even increments in t, as small as 1 pus re notsufficient to determine continuity (Ref. 17, Figs. 3-9): anincrease in tc of 1 pus uffices to convert prolongation intoabbreviation of cycle length. In fact, comparison of thecomputed voltage traces in these two instances revealsthat the membrane potential at the end of the pulse is 7PV more positive when abbreviation rather than prolon-gation of cycle length is produced. Since the amplitudeof membrane voltage noise in the aggregate is manytimes this value (12), it is not surprising that bothprolongation and abbreviation of cycle length can beseen at a fixed value of t, in the experiments (Fig. 4A).In fact, in a 15O-pm-diameter aggregate, the opening orclosing of only six ionic channels during the currentpulse may suffice to produce a change in the membranepotential of 7 PV and thus interconvert the two responsesshown in Fig. 4A (17). The situation in the model of theaggregate is probably similar to that which occurs in theHodgkin-Huxley model of the quiescent giant axon ofthe squid, where increments in the take-off potential oflo-l2 mV must be used to demonstrate that a discontin-uous all-or-none threshold phenomenon does not existin the model (6). In that case the continuous quasi-threshold phenomenon of FitzHugh occurs (8). Due tothe presence of membrane noise, further evaluation ofall-or-none phenomena in the aggregate would necessi-tate the formulation of an inherently stochastic modelrepresenting a population of single channels.

Winfree (31) has collected an impressive array of ex-amples showing that the phase-resetting behavior ofmany biological oscillators can be classified into twomain types: type 1 phase resetting is seenat a sufficientlylow stimulus strength, whereas type 0 phase resetting isseen at a sufficiently high stimulus strength. In type 1phase resetting T,/T, is a continuous function of 4 (Fig.3, A-C). In type 0 phase resetting YJTO is a discontin-uous function of 4 with a jump of -1 cycle length (Fig.3, E and F; see Refs. 16, 17, 31 for further discussion andmore precise definitions).Apart from our study, there appears to have been onlyone other study in which the transition from type 1 totype 0 resetting in a cardiac oscillator was systematicallyinvestigated (29). In that study, as the stimulus ampli-tude was increased, there was a direct transition fromtype 1 to type 0 phase resetting. This is in contrast tothe present findings, where we demonstrate type 1 phaseresetting at low amplitudes, type 0 phase resetting athigh amplitudes (Fig. 2C), and discontinuous, all-or-nonephase resetting (i.e., neither type 1 nor type 0) at inter-mediate amplitudes (Fig. 4)J One possible reason for this

The critical factor here is that after several cycles there is still aphase shift between the action potentials after prolonged and abbrevi-ated interbeat intervals (Fig. 4B: tc= 142 ms). Thu s the behavior inFig. 4 cannot be class ified as either type 1 or type 0 phase resetting(16, 17). As discu ssed above, if T1/To is a continuou s, very steep lydecreasing function in the neighborhood of tc= 141-143 ms, then thephase resetting would be type 1 but there is no way for us to resolvethis experimentally.


7/8


8/8

PHASE RESETTING OF EMBRYONIC HEART-CELL AGGREGATES H1305macroreentrant mechanism is not possible. Finally, 12.knowledge of the phase-resetting properties of the aggre-gates can be used to predict the effects of periodic stim- 13

lulation (15, 17, 19). In this way the origin of extremelyvaried, complex, and irregular rhythms observed duringperiodic stimulation of the aggregate and other cardiac 14*oscillators can be understood from the phase-resettingresponse to a single isolated stimulus. 15.

We thank Diane Colizza Guevara, Ken Rozansky, and RichardBrochu for preparing the aggregates and for excellent all-round labo- 16*ratory assistance. We also thank Sandra James and Christine Pamplinfor typing the manuscript and Peter Krnjevic for help in computerprogramming. 17.This work was supported by grants from the Canadian Heart Foun-dation, the Quebec Heart Foundation, and the Natural Sciences and 18lEngineering Research Council of Canada.M. R. Guevara was a recipient of a predoctoral traineeship from theCanadian Heart Foundation (198183).Received 30 December 1985; accepted in final form 7 July 1986. 19.

REFERENCES 20.

DEHAAN, R. L., AND L. J. DEFELICE. Electrical noise and rhythmicproperties of embryonic heart cell aggregates. Federation Proc. 37:2132-2138,1978.DEHAAN, R. L., AND H. A. FOZZARD. Membrane response tocurrent pulses in spheroidal aggregates of embryonic heart cells. J.Gen. Physiol. 65: 207-222, 1975.GILMOUR, R. F., JR., J. J. HEGER, E. N. PRYSTOWSKY, AND D. P.ZIPES. Cellular electrophysiologic abnormalities of diseased humanventricular myocardium. Am. J. CardioZ. 51: 137-144, 1983.GLASS, L., M. R. GUEVARA, J. BELAIR, AND A. SHRIER. Globalbifurcations of a periodically forced biological oscillator. Phys. Reu.A 29: 1348-1357,1984.GLASS, L., AND A. T. WINFREE. Discontinuities in phase-resettingexperiments. Am. J. Physiol. 246 (Regulatory Integrative Comp.Physiol. 15): R251-R258, 1984.GUEVARA, M. R. Chaotic Cardiac Dynamics (PhD thesis). Montreal,Canada: McGill Univ ., 1984.GUEVARA, M. R., AND L. GLASS. Phase locking, period doublingbifurcations and chaos in a mathematical model of a periodicallydriven oscillator: a theory for the entrainment of biological oscil-lators and the generation of cardiac dysrhythmias. J. Math. Biol.14: l-23,1982.GUEVARA, M. R., L. GLASS, AND A. SHRIER. Phase locking, period-doubling bifurcations, and irregular dynamics in periodically stim-ulated cardiac cells. Scienc e Wash. DC 214: 1350-1353, 1981.JALIFE, J., AND C. ANTZELEVITCH. Phase resetting and annihila-tion o f pacemaker activity in cardiac tissue. Science Wash. DC 206:695-697,1979.JALIFE, J., AND C. ANTZELEVITCH. Pacemaker annihilation: diag-nostic and therapeutic implications. Am. Heart J. 100: 128-130,1980.

1.

2.3.

4.

5.6.

7.

8.

9.

10.

11.

ANTZELEVITCH, C., AND G. K. MOE. Electrotonic inhibition and

249,1967.

summation o f impulse conduction in mammalian Purkinje fibers.Am. J. Physiol. 245 (Heart Circ. Physiol. 14): H42-H53, 1983.BEST, E. N. Null space in the Hodgkin-Huxley equations. A criticaltest. Biophys. J. 27: 87-104, 1979.BRISTOW, D. G., AND J. W. CLARK. A mathematical model ofprimary pacemaking cell in SA node of the heart. Am. J. Physiol.243 (Heart Circ. Physiol. 12): H207-H218, 1982.CASTELLANOS, A., R. M. LUCERI, F. MOLEIRO, D. S. KAYDEN, R.G. TROHMAN, L. ZAMAN, AND R. J. MYERBURG. Annihilation,entrainment and modulation of ventricular parasystolic rhythms.Am. J. Cardiol. 54: 317-322,1984.CHAY, T. R., AND Y. S. LEE. Impulse responses of automatic ity inthe Purkinje fiber. Biophys. J. 45: 841-849, 1984.CLAY, J. R. Monte Carlo simulation of membrane noise: an analysisof fluctuations in graded excitation of nerve membrane. J. Theor.Biol. 64: 671-680, 1977.CLAY, J. R., AND R. L. DEHAAN. Fluctuations in interbeat intervalin rhythmic heart-cell clusters: role of membrane voltage noise.Biophys. J. 28: 377-389, 1979.CLAY, J. R., M. R. GUEVARA, AND A. SHRIER. Phase resetting ofthe rhythmic act ivi ty of embryonic heart cell aggregates. Experi-ment and theory. Biophys. J. 45: 699-714,1984.COLIZZA, D., M. R. GUEVARA, AND A. SHRIER. A comparative studyof collagenase- and trypsin-dissociated embryonic heart cells: reag-gregation, electrophysiology, and pharmacology. Can. J. Physiol.Pharmacol. 61: 408-419, 1983.CRANEFIELD, P. F., AND R. S. ARONSON. Initiation of sustainedrhythmic act ivi ty by single propagated action potentials in caninecardiac Purkinje fibers exposed to sodium-free solution or to oua-bain. Circ. Res. 34: 477-481, 1974.DEHAAN, R. L. Regulation of spontaneous act ivi ty and growth ofembryonic chick heart cells in tissue culture. Deu. Biol. 16: 216-

21.

22.

23.

24.

25.26.

27.

28.

29.

30.31.

JALIFE, J., A. J. HAMILTON, V. R. LAMANNA, AND G. K. MOE.Effect s of current flow on pacemaker act ivi ty of the isolated kittensinoatrial node. Am. J. Physiol. 238 (Heart Circ. Physiol. 7): H307-H316,1980.JALIFE, J., AND G. K. MOE. Effect of electrotonic potentials onpacemaker act ivi ty o f canine Purkinje fibers in relation to para-systole. Circ. Res. 39: 801-808, 1976.MATHIAS, R. T., L. EBIHARA, M. LIEBERMAN, AND E. A. JOHNSON.Linear electrical properties of passive and active currents in spher-ical heart cell clusters. Biophys. J. 36: 221-242, 1981.PARSHINTSEV, V. V. Arrhythmia due to a single electric shock ina heart cell culture. Biophys. J. 18: 1191-1193, 1973.ROBERGE, F. A., AND R. A. NADEAU. Analogies between relaxationoscillators and biological pacemakers. Can. Electron Conf. IEEEPaper 65054, Cat. No. F17, 1965, p. 64-65.SANO, T., T. SAWANOBORI, AND H. ADANIYA. Mechanism ofrhythm determination among pacemaker cells of the mammaliansinus node. Am. J. Physiol. 235 (Heart Circ. Physiol. 4): H379-H384, 1978.SCOTT, S. W. Stimulation Simulations of Young Yet CulturedBeating Hearts (PhD thesis). Buffalo, NY: State Univ. of NewYork, 1979.

-A- a -7

VAN MEERWIJK, W. P. M., G. DEBRUIN, A. C. G. VAN GINNEKEN,J. VANHARTEVELT, H. J. JONGSMA, E. W. KRUYT, S. S. SCOTT,AND D. L. YPEY. Phase resetting properties of cardiac pacemakercells. J. Gen. Physiol. 83: 613-629, 1984.WEIDMANN, S. Eff ect of current flow on the membrane potentialof cardiac muscle. J. Physiol. Land. 115: 227-236, 1951.WINFREE, A. T. The Geometry of Biological Time. New York:Snringer-Verlae. 1980.

michael r. guevara et al- phase resetting of spontaneously beating embryonic ventricular heart cell...

Documents