mechanisms of stretch-induced changes in [ca21 in rat...

Mechanisms of Stretch-Induced Changes in [Ca21]i inRat Atrial Myocytes

Role of Increased Troponin C Affinity and Stretch-Activated Ion Channels

Pasi Tavi, Chunlei Han, Matti Weckstro¨m

Abstract—To study the effects of stretch on the function of rat left atrium, we recorded contraction force, calciumtransients, and intracellular action potentials (APs) during stretch manipulations. The stretch of the atrium wascontrolled by intra-atrial pressure. The Frank-Starling behavior of the atrium was manifested as a biphasic increase ofthe contraction force after increasing the stretch level. The development of the contraction force after step increase ofthe stretch (intra-atrial pressure from 1 to 3 mm Hg) was accompanied by the increase in the amplitude of the calciumtransients (P,0.05, n54) and decrease in the time constant of the Ca21 transient decay. The APs of the individualmyocytes were also affected by stretch; the duration of the AP was decreased at positive voltages (AP duration at 15%repolarization level,P,0.001; n513) and increased at negative voltages (AP duration at 90% repolarization level,P,0.01; n513). To study the mechanisms causing these changes we developed a mathematical model describing [Ca21]i

and electrical behavior of single rat atrial myocytes. Stretch was simulated in the model by increasing the troponin (TnC)sensitivity and/or applying a stretch-activated (SA) calcium influx. We mimicked the Ca21 influx by introducing anonselective cationic conductance, the SA channels, into the membrane. Neither of the 2 plausible mechanosensors(TnC or SA channels) alone could produce similar changes in the Ca21 transients or APs as seen in the experiments. Themodel simulated the effects of stretch seen in experiments best when both the TnC affinity and the SA conductanceactivation were applied simultaneously. The SA channel activation led to gradual augmentation of Ca21 transients,which modulated the APs through increased Na1/Ca21-exchanger inward current. The role of TnC affinity change wasto modulate the Ca21 transients, stabilize the diastolic [Ca21]i, and presumably to produce the immediate increase of thecontraction force after stretch seen in experiments. Furthermore, we found that the same mechanism that caused thenormal physiological responses to stretch could also generate arrhythmogenic afterpotentials at high stretch levels inthe model.(Circ Res. 1998;83:1165-1177.)

Key Words: stretchn myocyten Frank-Starlingn Ca21n action potential

The stretch-induced changes in heart muscle are prototyp-ically manifested as an increase in the contraction force,

the well-known Frank-Starling mechanism.1 Although it isknown that mechanical stimulation can influence the freeintracellular calcium,2–5 contraction force,6 and electrical ac-tion of the myocytes,7,8 the underlying mechanisms have notbeen resolved. It has been reported that the stretch-dependentchanges in the cardiac contraction force has 2 components.9

Immediately after stretch the contraction force is increased.This increase is followed by additional slow increase in force.Increase of the muscle length produces a gradual increase inCa21 transient amplitude.10 The stretch sensitivity of troponinC (TnC)11,12 and mechanical changes in the crossbridgeattachments, like the reduction of double thin-filament over-lap13–15 might explain the fast increase in contraction force,causing additional buffering of Ca21 by the contractile ele-ment and increase in contraction force. However, it is not

possible to augment the Ca21 transients by the increasedsensitivity of TnC. A complementary explanation for theincrease of the Ca21 transients during stretch would beactivation of stretch-activated (SA) channels, first reported byGuharay and Sachs,16 which have also been found in cardiacmyocytes.17–22 The aim of the current study was to define thestretch-induced changes in the isolated rat atrium in whichstretch could be controlled by intra-atrial pressure. From thephysiological point of view the plausible candidates (TnC andSA channels) for the mechanosensation in the heart are noteasy to study. Usually ion channel function is studied byblockers or activators of the channel in question. In the caseof SA channels, selective blockers are not known presently.The SA channel blockers previously used are fairly unspe-cific. For example, gadolinium blocks SA channels23 but alsoL-type Ca21 channels24 and delayed rectifier K1 channels.25

The function of the TnC is also difficult to study in intact (or

Received June 8, 1998; accepted September 16, 1998.From the Departments of Physiology and Physical Sciences/Division of Biophysics and Biocenter Oulu, University of Oulu, Oulu, Finland.Correspondence to Matti Weckstrom, MD, PhD, Department of Physiology, University of Oulu, Kajaanintie 52A, FIN-90220 Oulu, Finland. E-mail

[email protected]© 1998 American Heart Association, Inc.

Circulation Researchis available at http://www.circresaha.org

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semi-intact) cardiac tissue. The central role of TnC incontraction makes it fairly inaccessible to study by physio-logical methods. It is also difficult to distinguish the effects ofTnC on the function of the cardiac cells from other regulatorsof the contractile element (eg, troponins I and T).

The role of SA channels in the generation of the patholog-ical effects of stretch has been widely studied previously.26,27

From the physiological point of view, if SA channels exist inthe cardiac myocytes, the major function of these channelswould be the participation in the normal stretch-dependentchanges in the heart muscle (such as Frank-Starling [F-S]relation), rather than generation of pathological phenomena.On the basis of this hypothesis, we studied the influence ofstretch on the APs, contraction force, and intracellular [Ca21]i

in the rat atrium. To keep the stretch in the range of the risingphase of the Frank-Starling relation, we used only smallstretch stimuli. To complement the experimental part of thestudy, we developed a mathematical model by which wecould further study the role of TnC and SA channels in thestretch-induced changes at the level of individual myocytes.We found that during the stretch activation of rat atrium,which included prolongation of APs, biphasic increase of thecontraction force, and augmentation of the Ca21 transients, atleast 2 different mechanisms were involved. We show that themodel could produce similar changes in Ca21 balance andAPs as seen in experiments only when a stretch-dependentCa21 influx (mimicking SA channel activation) was includedin the simulation. The model simulations resembled theexperiments closest when stretch was simulated by SAchannel activation and increased Ca21 affinity of TnC.

Materials and MethodsAnimals, Preparation, and SuperfusionMale Sprague-Dawley rats (n560) weighing 290 to 400 g were used.The care and use of animals were approved by the committee oflaboratory animal experimentation at the University of Oulu. Theywere kept at 20°C to 22°C and had free access to tap water andstandard food. The rats were decapitated, and their hearts wererapidly removed and placed in oxygenated cool (25°C) buffersolution consisting of (in mmol/L) NaCl 137, KCl 5.6, CaCl2 2.2,HEPES 5.0, MgCl2 1.2, and glucose 2.5 (pH 7.4), which was alsoused for superfusion of the atrial preparation.

The experimental model used in this study was the isolated ratatrial appendix, prepared as described previously.28 Briefly, anX-branch polyethylene adapter was inserted into the lumen of the leftauricle, and the tissue was placed in a constant-temperature (37°C)organ bath. Another tube with smaller diameter was inserted insidethe adapter to carry perfusate inflow into the lumen of the auricle.The outflow from the lumen came from 1 cross-branch of theX-cannula. The stretch of the atrium was produced by changingintra-atrial pressure. Pressure inside the atrium was increased byincreasing the height of the outflow tube. The other cross-branch ofthe X-cannula was connected to a pressure transducer (TCB 100,Millar Instruments, Inc), so that the pressure in the lumen of the auriclecould be recorded. Inflow and outflow (3 mL/min) both to the auriclelumen and to the organ bath with constant temperature were controlledby a peristaltic pump (7553-85, Cole-Parmer Instrument Co).

Electrophysiological Recordings and Data AnalysisMembrane potentials were recorded using glass microelectrodesfilled with a solution of 2 mol/L potassium acetate and 5 mmol/LKCl, pH 7.0. The resistances of the electrodes in tissue were 70 to120 MV. A chloride-treated silver wire, used as a reference, was

placed in contact with the superfusion medium in the organ bath. Theelectrode holder connected to a micromanipulator was a spring ofchloride-treated silver wire (diameter 0.3 mm). The atrial appendix(being the left one) was quiescent unless stimulated electricallythrough bipolar Ag/AgCl electrodes placed in contact with theauricle. Electrical stimulation (steps of duration 1 ms, 50% overthreshold voltage) was provided by a stimulator (S44; Grass Instru-ments Co). All electrical signals were amplified with an intracellularamplifier (Dagan 8100-1; Dagan Co) and stored by a data recorder(Biologic DTR-1800; Biologic Ltd). Data analysis was done with DTVEE (Data Translation Inc) and MATLAB (The Math Inc) pro-grams. Sampling frequency was 3 kHz in all recordings.

Calcium MeasurementsTo record intracellular Ca21 transients from the Indo 1–loaded ratatria, a fiber optic silica cable was led through the bottom of theperfusion chamber to make contact with the tissue. In the detectionend, the fiber cable consists of'100 unorganized fibers (diameter100 mm), which are further divided into 3 individual fiber bunchesconsisting of'30 individual fibers each. One branch guided the355-nm filtered excitation light to the tissue provided by 75-W xenonlight source (Hamamatsu), and the 2 remaining branches conductedthe emitted light that was filtered (40565 nm and 49565 nm) anddetected with photomultiplier tubes (Hamamatsu). The emissionsignal was further amplified (38) and filtered with an adjustableKemo filter (Kemo Corp) at 50 Hz. The Indo 1 emission ratio(405/495) was calculated online from an A/D-converted (DataTranslation) signal by Testpoint (Capital Equipment Corp) custom-created software. The atrium was paced with 2 platinum electrodesat 1 Hz.

Loading the Atria With Indo 1For Ca21 measurements the left atrial preparation was attached, priorto loading, to the perfusion system to measure the autofluorescencefrom each atrium. The autofluorescence at both emission wave-lengths was determined and then subtracted from the signals afterloading. Together with the autofluorescence the contraction force(developed pressure) was measured at the low pressure (1 mm Hg),which was compared with the contraction force after loading. ForIndo 1 AM loading, the preparation connected to the plastic tube wasattached to a separate loading chamber. In this chamber, the atriawere superfused for 25 to 40 minutes (flow 7 mL/min) with HEPESbuffer (4 mL) containing 10mmol/L Indo 1 AM dissolved to 100mLDMSO with 20% Pluronic, 0.5 mmol/L probenecid, and 1.5% BSA.To avoid loading of the intracellular organelles such as sarcoplasmicreticulum (SR) and mitochondria, the temperature in the chamberwas kept between 25°C and 30°C during the entire loading period.After loading the fluorescence was'20 times greater than theautofluorescence before loading. The contraction force (developedpressure), which was 1 mm Hg before loading, was 3.160.4 and3.1760.4 mm Hg after loading (NS, n515). This indicates that Indoitself does not buffer calcium ions enough to influence the contrac-tion. It has been shown previously that when epifluorescence of theheart muscle is used in estimation of the intracellular calcium of themyocytes, part of the fluorescence signal may originate from cellsother than myocytes,29 forming a possible source of error. Whencardiac tissue is loaded with fluorescence indicators such as Fura-2and Indo 1 through coronary arteries, a great portion of theepifluorescence comes from the endothelial cells.29 Here we tried toavoid this by not using the coronary circulation in loading; insteadwe used direct perfusion of the tissue. The source of fluorescencewas also under visual control (ie, when the atria were attached to theperfusion system the areas of clearly greater fluorescence intensitywere avoided, and the atria were measured from the areas with lowtotal fluorescence intensity and no visually detectable “hot spots”).In some preparations the contraction and stretch of the tissue causeda prominent movement artifact, and these atria were not used.

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Mathematical ModelThe model used in this study is based on that developed by Luo andRudy.30–32Since the original model was designed to model the guineapig ventricular cell, we had to make extensive modification to fit themodel to our and previously published experimental results from ratatrial myocytes. Together with the species-specific modifications(see Appendix), we introduced a more complex method of Ca21

handling into the model on the basis of recent reports. The calciumrelease in atrial myocytes is a combination of the release from 2different compartments of the SR.33,34 The basic idea of this 2-stepCa-release model is that the calcium entering through L-typechannels triggers calcium release from the first release compartment(peripheral SR), and the Ca21 released from the first compartmenttriggers release from the second compartment (corbular SR) in anall-or-none manner. The trigger threshold of the second compartmentwas set at the value equal to the half of the calcium peak of normalrelease from the first compartment, with the time constants ofactivation and inactivation 40 and 10 ms, respectively. Time delaybetween release from first and second compartments was 5 ms basedon the calcium wave propagation velocity and calcium gradients inatrial myocytes.33,35,36 These adjustments made the calcium releasefrom the second compartment slower than from the first compart-ment, consistent with experimental data.34

Simulation of Stretch by the ModelThe SA channels in the cardiac myocytes have reportedly a nearlinear voltage dependence,22 no adaptation,37 and nonselectivity overcations.19 The reversal potential of the SA channel current is –3.2 mVin rat atrial myocytes.19 The SA channel formalism was adapted fromprevious models,38 with small modifications.

The SA channel current is given elegantly by Sachs38 by thefollowing equation:

(1) ISAC5~V2Vrev!gr

11K exp@2a~L2L0!#

whereISAC is the current density (mA/mF), V is membrane potential,Vrev is reversal potential (–3.2 mV),K is equilibrium constant (100),L is sarcomere length,L0 is minimum sarcomere length (1mm), a isthe parameter defining the stretch sensitivity (3),r is channel density(0.015/mm2), and g is single-channel conductance (25 pS). Theiteration of the SA current was based on our experimental data. Tosimulate the stretch effects seen in our experiments, only 5% of thepreviously suggested value38 (0.3/mm2) of the SA channel currentwas needed in the model. To simulate stretch of the rat atrium causedby the increase of the intra-atrial pressure from 1 to 3 mm Hg,increase of the current density during diastole from –0.03 to –0.32mA/mF was used. In our experiments we have not measured thesarcomere lengths. However, in the model (using the definitions ofSachs38), this SA channel current increase corresponds to an increaseof sarcomere length from 1.2 to 1.9mm, increasing the openprobability of the SA channels from 0.03 to 0.16.

Gulati et al12 showed that the calcium affinity of the contractileelement increased after a length change, wherebyKd (for Ca21) of theTnC decreased 42% when the sarcomere length of skinned cardiacmuscle was increased from 1.7 to 2.2mm, which almost correspondsto the overall sarcomere length change during the rising phase of theF-S relation in rat trabeculae.39 According to these observations, weapproximated that the overall increase of the TnC affinity during therising phase of the F-S relation is'50%. Knowing that the risingphase of the F-S relation in rat left atrium is within intra-atrialpressure between 0 and'10 mm Hg,40 we approximated that theincrease of the intra-atrial pressure in our experiments from 1 to3 mm Hg produces a 25% decrease of theKd in the TnC. This valuewas used in modeling the stretch caused by increase of the intra-atrialpressure from 1 to 3 mm Hg (Figure 1). The simulation of the stretchin the model was based on the following assumptions. First, therelation of the TnC affinity change between 0% and 50% increaseand sarcomere length is linear. Secondly, the SA channel currentdensity (open probability of the channel) increases with increasedsarcomere length, giving the maximum open probability of the

channel at a sarcomere length that produces maximal developedtension. Thus, the current density increase from 0% to 100% isachieved during the rising phase of the F-S relation in the model.Figure 1 shows the SA current density and TnC affinity change atdifferent sarcomere lengths in the model. In extrapolating to patho-logical stretch levels we used SA channel current density from 0.2 to1.54 mA/mF, and at the same time the TnC affinity was increasedfrom 20% to 50%. The assumptions are based on the scarcepublished data on the mechanisms, and, if the relationships betweenthe modeled components of stretch sensitivity are more complex, thiswould probably introduce more complex behavior into the model butdoes not change the basic results.

MaterialsHEPES was obtained from Sigma; KCl, glucose, CaCl2, and MgCl2from Merck; NaCl and potassium acetate from FF-Chemicals AB;Indo 1-AM, poloxamer, and probenecid (p-[dipropylsulfamoyl]-benzoic acid) from Molecular Probes Europe BV.

Statistical AnalysisStatistical testing was done by the SPSS (SPSS Inc) and SigmaStatprograms (Jandel Scientific). The AP data were tested with 1-wayANOVA. The data from contraction and Indo fluorescence weretested with a pairedt test. In all cases,P values less than 0.05 wereconsidered statistically significant. Variances are expressed as6SEM.

Figure 1. Modeled relationships between sarcomere length, theSA current (SA current density), TnC affinity, and the pressure-induced stretch in the experiments. Dashed line shows approxi-mations of the TnC affinity for Ca21; solid line shows modeledSA current density, both in function of the sarcomere length inthe model. F, demonstration of how SA current is connected tothe stretching pressure used in the experiments. f, values ofTnC affinity used to model the stretch effects. See text fordetails.

Stretch-Induced Changes in AP Parameters

1 mm Hg(n59)

3 mm Hg(n513)

RP, mV 275.160.7 277.360.7

Amplitude, mV 95.961.2 99.361.4

APD15%, ms 4.860.2 3.360.3***

APD60%, ms 17.360.2 17.560.6

APD90%, ms 43.460.8 53.462.3**

Variances were tested by 1-way ANOVA. Asterisks denote the statisticalsignificance compared with AP parameters in 1 mm Hg (**P,0.01;***P,0.001).

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ResultsStretch-Induced Changes in APsIn the first series of experiments we investigated the effects ofa stained moderate stretch on APs of rat atrial myocytes. Thetissue was stretched by the intra-atrial (diastolic) pressure.Criteria for acceptable experiments were a stable recordingwith a resting potential (RP) of least –70 mV and anovershoot of the AP of at least 10 mV. The atria were kept atconstant pressure (1 or 3 mm Hg) for 5 minutes untilrecordings were started. At low pressure (1 mm Hg), myo-cytes with RP of –75.160.7 mV generated APs (n59) withamplitude of 95.861.2 mV. When the pressure was3 mm Hg, AP duration at 90% repolarization level (APD90%)and APD10% decreased (Table, Figure 2).

Because the sustained stretch changed the AP shape, werecorded APs during the pressure manipulations to observethe time course of the changes. These recordings were foundto be extremely difficult, and only a very few of the attemptswere successful. Before each recording the atrium was kept atsteady pressure (1 mm Hg) until acceptable impalement(stable recordings, RPs at least –70 mV and overshoot at least10 mV) was achieved. After the recording had been stable forat least 20 s, pressure inside the atria was gradually increased

from 1 to 3 mm Hg over 10 seconds and then kept constant(3 mm Hg) for at least 1 minute. Figure 3 shows a represen-tative trace (out of 3 successful experiments, in which theimpalement was still stable after at least 1 minute of stretch)of the changes that increased stretch (from 1 to 3 mm Hg)causes in the APs of myocytes. Immediately after the increaseof stretch the shape of the APs was changed. The durationdecreased at positive voltages (at 10% repolarization levelfrom 3.75 to 3.25 ms) and increased at negative membranepotentials (at 90% repolarization level from 43 to 47 ms).After 60 seconds of onset of stretch, some of the changes inAP were even more prominent (APD90%, 52.5 ms). All cellsstudied were able to maintain fairly constant RP duringpressure manipulations. Depolarization of the measured po-tential (during diastole) was always associated with thechanges in the cell-electrode impalement (resistance andcapacitance) caused by the electrode leaving the cell.

To see whether the AP lengthening corresponds to thedevelopment of the contraction force after stretch, the APD90%

was plotted together with the change in contraction force.Figure 4 shows that the development of the slow increase offorce (within 1 minute) in rat atrial tissue is accompanied bythe lengthening of the AP (APD90%) of the individual myo-cytes with a similar time course.

Figure 2. The effects of sustained moderate stretch on APs ofrat atrium. Ten APs from each cell were averaged. The RPs ofthe recordings were set to be the same to facilitate comparisonof AP shape. The corresponding AP parameters are presentedin the Table with statistical analysis. Solid line, pressure1 mm Hg (n59 cells); dashed line, pressure 3 mm Hg (n513cells).

Figure 3. A representative intracellularvoltage recording from rat atrium withstretch. The intra-atrial pressure wasgradually increased from 1 to 3 mm Hg in10 seconds (bottom trace). The middletrace shows the intracellular recordingwith pacing frequency of 2 Hz. Traces attop show APs (average of 10) from thesame recording before stretch (A; pres-sure 1 mm Hg), after 10 seconds ofstretch increase (B; pressure 3 mm Hg),and at 1 minute of stretch (C; pressure3 mm Hg).

Figure 4. Changes in developed pressure (bottom) and APD90%,

(top) during the stretch of the rat atrium by increasing the intra-atrial (diastolic) pressure from 1 to 3 mm Hg. On APD graph(top), solid circles show the durations measured from each indi-vidual AP.



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Effects of Stretch on Atrial Contraction andCa21 TransientsFigure 5 shows the effect of stretch on the contraction forceand the calcium transients in the rat atrium. When theintra-atrial pressure was increased from 1 to 3 mm Hg, thecontraction force was increased biphasically. The immediateincrease was followed by a secondary, slower increase inforce, as can be seen from the example recording in theFigure 5A. The Ca21 transients (as Indo 1 fluorescence ratio)show that the increase of contraction force is accompanied byan increase in amplitude of the calcium transients (Figure5B), without any change in the diastolic Indo 1 fluorescenceratio (NS, n54). The pooled and normalized data in Figure5C show the contraction force at different times after onset ofstretch. Although increase of the contraction force is fast (ie,10 seconds of stretch more than doubles the force), there isstill a significant increase between 10 seconds and 2 minutesafter stretch (P,0.01, n54). This slower increase of force islikely to be due to the increase of Ca21 transients that werealso augmented during the same time scale (Figure 5D;P,0.01, n54).

On the basis of the data presented in the Figure 5C and 5D,it is evident that most of the effects of stretch are actuallymanifested during the 10 seconds after the onset of stretch. Tostudy the time courses of these changes, we analyzed the first10 Ca21 transients and contraction pulses from each recording

(n54). It can readily be seen from Figure 6A and 6B that thedevelopment of contraction force is faster than the increase ofthe calcium transient amplitude. This indicates that the fastcomponent of the contraction force development is not due tothe increase of the calcium transient amplitude, but is prob-ably caused by the increased sensitivity of the contractileelement to Ca21. If this were true, increased buffering of theCa21 by the contractile element should alter the shape of theCa21 transients. The 1-exponential fits to the decay of Ca21

transients revealed that, in fact, the decay becomes faster afterstretch (Figure 6C). However, it has been shown that thedecay of the Ca21 transient is accelerated by increased Ca21

transient amplitude.41 Because of this, the effect of Ca21

transient amplitude had to be estimated in order to use thedecay as an indicator of the Ca21 buffering of the cells. As therate of free Ca21 decline increases in a parabolic manner,41

proportional to [Ca21]2, we calculated the ratio between thedecay and the square of the amplitude of the Ca21 transients.In theory, any intervention that increases buffering of theCa21 should reduce the ratio, but if the changes in the decayare caused by bigger Ca21 transients, this ratio is not changed.Figure 6D shows that the decay of the Ca21 transient isaccelerated during the first 10 seconds after the onset of thestretch, with no significant change thereafter (NS, n54),independently of the amplitude of the Ca21 transients. This islikely to be caused by the stretch sensitivity of the contractileelement.

Model PredictionsThe main findings of the experimental part of the study can besummarized as follows. Moderate stretch causes increase inthe amplitude of the Ca21 transients and decrease of the timeconstant of the decay of the transients without a significant

Figure 5. Stretch-induced changes in the contraction and Ca21

transients in the rat atrium. A, Example contraction pulses(developed pressure) before and 10 seconds and 2 minutesafter increase of the diastolic intra-atrial pressure from 1 to3 mm Hg. B, Example Ca21 transients (as Indo 1 ratio) beforeand 10 seconds and 2 minutes after increasing the diastolicintra-atrial pressure from 1 to 3 mm Hg. C, Pooled and normal-ized (to control, ie, prestretch) data from 4 experiments showingthe time course of the contraction development after stretch. Pvalue indicates the statistical difference between contraction at10 seconds and 2 minutes after onset of stretch obtained bypaired t test (n54). D, Pooled and normalized data from 4experiments showing the time course of the relative changes inthe Ca21 transient amplitude after stretch. P value indicates thestatistical difference between contraction at 10 seconds and 2minutes after onset of the stretch as above (n54).

Figure 6. Relative changes in Ca21 transient amplitude (A), con-traction force (developed pressure B); Ca21 transient decay(1-exponential fit; C), and the ratio between the decay and thesquare of the Ca21 transient amplitude (D). The first dot in eachfigure represents the unstretched control (normalized to 1). Thelines in every figure are (sigmoidal) fits done for convenience.Each dot represents the mean value from 4 separateexperiments.



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change in the diastolic [Ca21]i. These changes were accom-panied by lengthening of the APs of the myocytes and abiphasic increase of the contraction force of the atrium. In thesecond part of the study we tried to reproduce similar changesin the Ca21 balance and APs by modulating the TnC affinityand/or calcium influx mimicking SA channel activation in themodel.

Role of TnCOne candidate for mechanosensation in heart cells is the TnC,calcium-binding part of the contractile machinery, which isknown to be sensitive to stretch.11,12 We increased the TnCaffinity to Ca21 by decreasing the dissociation constant (Kd)of TnC by 25% in our model (see Materials and Methods).This caused a biphasic behavior of the Ca21 transients. Firsttransients were smaller, but amplitude stabilized near thecontrol value (Figure 7A) within 1 minute. Even when thesystolic [Ca21]i had returned to the control value, the decay ofthe Ca21 transient was faster (time constant decreased from118 to 105 ms; Figure 7C). When control APs were comparedwith steady-state APs after a simulated stretch, only modestchanges were observed, the most prominent change being thesmall increase of the APD90% (12.4 ms; Figure 7B). Theincreased Ca21 affinity of the TnC modulated slightly theCa21 dependent currents, the peak value of the L-type Ca21

current (Figure 7D) was increased from –10.3 to –10.5mA/mF, and the inward current of the Na1/Ca21 exchanger(Figure 7E) was decreased from –1.09 to –1.05mA/mF. Thisresult indicates that the TnC affinity change alone cannot

produce similar changes as observed in experiments, since theTnC affinity change could not augment the Ca21 transients orlengthen the APs.

Role of SA ChannelsWhen stretch of the myocyte was simulated by applying theSA channel conductance into the cell membrane in ourmodel, the amplitude of the calcium transients were graduallyincreased (Figure 8A). The activation of a cation-selective SAchannel increased the systolic [Ca21] gradually from 0.88 to1.04 mmol/L within 1 minute (115.4%). The decay of thecalcium transients decreased (as measured by the time con-stant of the 1-exponential fits) from 115 to 114 ms (Figure8C). Only a small change in the diastolic [Ca21] was observed(Figure 8A). Greater Ca21 transients increased the late dura-tion of the APs (Figure 8B), the time course of the APlengthening being related to the increase of the amplitude ofthe calcium transients. The APD90% increased from 52.2 to61.4 ms within 1 minute after the increased SA channelcurrent. This was probably due to the increase of the inwardcurrent carried by Na1/Ca21 exchanger (Figure 8E), whichwas increased from –1.09 to –1.16mA/mF. Bigger Ca21

transients decreased the peak value of the L-type Ca21 current(by increasing inactivation) from –10.3 to –10.1mA/mF(Figure 8D) and made the decay of the current a little faster.

Combination of SA Channel and TnC EffectsNeither of the 2 candidates of the mechanosensation (SAchannels and TnC) could faithfully produce similar changesin the model cell as seen in experiments. The TnC affinitychange could not produce the gradual increase of the ampli-tude of the Ca21 transients or increase of the APD90%. The

Figure 7. Predictions of the model when stretch only increasesthe Ca21 affinity of the TnC. Solid lines show the unstretchedsituation (1); dashed lines depict the change after 1 minute ofstretch (2). A, Ca21 transients during simulation; B, APs; C,Detail of Ca21 transients, with time constants of 1-exponentialfits; D, L-type Ca21 current; E, Na1/Ca21 exchange current.Observe the difference in time scale between panels B and D(left) and panels C and E (right).

Figure 8. Predictions of the model when stretch only increasesthe current density of the SA channels. Solid lines show theunstretched situation (1); dashed lines depict the change after 1minute of stretch (2). A, Ca21 transients during simulation; B,APs; C, Detail of Ca21 transients, with time constants of1-exponential fits; D, L-type Ca21 current; E, Na1/Ca21

exchange current. Observe the difference in time scale betweenpanels B and D (left) and panels C and E (right).



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activation of the SA channels produced both effects, but notthe prominent change in the decay of the transients. Further-more, the SA channel activation cannot explain the fastincrease of the contraction force seen in experiments, since itcaused a slow and gradual augmentation of Ca21 transientsduring stretch. To better fit the model predictions to experi-mental findings, we combined these 2 mechanisms in the nextround of modeling (Figure 9). When the stretch was simu-lated by increasing the TnC affinity together with the activa-tion of the SA current, the Ca21 transient amplitude graduallyincreased by 20.2% from 0.88 to 1.09mmol/L (Figure 9A and9C). The increase of the amplitude of the Ca21 transients wasaccompanied by the decrease of the time constant of thedecay of the transients from 119 to 96 ms (Figure 9C).Increased calcium mobilization during the AP caused asimultaneous lengthening of the AP (Figure 9B). The APD90%

increased from 52.2 to 63.8 ms within 1 minute, and timecourse of the AP lengthening was related to the increase ofthe calcium transients. Since the peak value and the decay ofthe L-type Ca21 current was unaffected (Figure 9D), we mayconclude that the increase of the inward current carried byNa1/Ca21 exchanger from –1.09 to –1.19mA/mF (Figure 9E)increased the late duration of the APs.

Role of SRIf the Ca21 release kinetics is not altered, the amount of Ca21

in SR contributes prominently to the released Ca21 duringexcitation.42 Figure 10 shows how different strategies of the

stretch simulation (TnC affinity, SA channels, or both)influence the amount of Ca21 in the SR. When stretch wassimulated solely by increasing the TnC affinity by 25%(Figure 10A), the SR Ca21 content was affected only slightly.The diastolic Ca21 in the SR increased from 1.65 to1.69 mmol/L within 1 minute. Activation of SA channelswithout any change in TnC affinity (Figure 10B) increasedthe diastolic SR Ca21 content from 1.65 to 1.79 mmol/L. Theeffects of TnC affinity change and activation of SA channelswere additive (as shown in Figure 10C); SR calcium contentincreased from 1.65 to 1.88 mmol/L. This modeling resultindicates that augmentation of the Ca21 transient in the modelduring simulated stretch is due to the increased amount ofCa21 in the SR. Furthermore, SA channel activation does notcause direct increase of the Ca21 transient, but the effect ismediated by the Ca21 release from SR.

Electrical Changes Caused by the Simulation ofthe StretchSince the combination of SA channel activation and theincreased affinity of TnC simulated fairly well the effects ofstretch observed in the experiments, we investigated whetherthis approach causes simultaneous changes in Ca21 transientsand APs and whether the time course of this change is similarto those in the experiments. Figure 11 shows the AP train (A),calcium transients (B), and APD90% (C) when the stretch wassimulated by increasing the SA channel current and calciumaffinity of the TnC. The augmentation of the Ca21 transientlengthened the APs by 10 ms within 1 minute, as indicated bythe APD90%, in line with our experimental findings (Figures 2through 4).

Pathological Effects of StretchIn addition to the physiological effects, the stretch of thecardiac tissue also causes pathological phenomena. It isknown that intensive stretch can trigger arrhythmias caused

Figure 9. Predictions of the model when stretch both increasesthe Ca21 affinity of the TnC and increases the current density ofthe SA channels. Solid lines show the unstretched situation (1);dashed lines depict the change after 1 minute of stretch (2). A,Ca21 transients during simulation; B, APs; C, Detail of Ca21 tran-sients, with time constants of 1-exponential fits; D, L-type Ca21

current; E, Na1/Ca21 exchange current. Observe the differencein time scale between panels B and D (left) and panels C and E(right).

Figure 10. Comparison of the modeled Ca21 content in SR in 3stretching situations, when the TnC affinity was changed (A),when SA current density is increased (ISAC) (B), and when bothare increased (C).



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by early or delayed afterdepolarizations of the membranepotential.40 The mechanism suggested to be responsible forthese arrhythmias is the calcium overload caused by stretch.43

We investigated whether the same mechanisms that cause thephysiological effects of stretch could be responsible for thepathological stretch-induced changes in the function of theheart. To do this, we simulated the effects of incrementalstretch on the function of the model cell. It is natural toassume that if a cationic current through SA channels, withreversal potential more positive than the RP, is activated, itshould cause a depolarization of the membrane potential.Because SA channels also pass Ca21 ions,19 the depolarizationwould be followed by an increase of the [Ca21]i. Both of theseeffects were seen when SA current density was increasedgradually from 0.1 to 1.6mA/mF (Figure 12A and 12B; seealso Materials and Methods for details), at the same time thatthe TnC affinity was increased from 20% to 50%, respec-tively. The RP depolarized up to –68 mV (from –80.5 mV)at the same time when diastolic [Ca21]i was increased from0.1 to 0.16mmol/L.

Figure 13 shows that the model can produce an arrhyth-mogenic effect when the SA channel current density is 8times as high as needed in the model to produce thephysiological effects seen in our experiments. Similarly, as inother simulations, augmentation of the Ca21 transients (Figure13B) modulated the APs (Figure 13A) through increasedNa1/Ca21 current (Figure 13D). When 80% of the channelspresent in our model were open, the augmented Ca21 transientreduced the L-type Ca21 current (Figure 13C) from –10.4 to–8.2 mA/mF. Because the Na1/Ca21-exchanger inward cur-rent was increased from –1.2 to –2.6mA/mF, it generated anafterpotential that resembles the early afterdepolarizations ofthe atrial myocytes.44 These results show that the samemechanisms that mimic the physiological effects of stretchcan also produce the arrhythmogenic changes in the functionof myocytes.

DiscussionThe present study demonstrates that stretch, in this casediastolic pressure, has a wide variety of actions in isolated ratatrium. The experimental part of the study shows thatcontractile function has a biphasic response to stretch, asso-ciated with augmentation of the Ca21 transients, without asignificant change in the diastolic [Ca21]i. Diastolic calciumconcentration remains fairly constant because the Ca21 buff-ering power of the cell is increased, indicated by the fasterdecay of the Ca21 transients during stretch. APs of themyocytes reflect the changes in Ca21 transients and contrac-tion force. The most prominent change in APs during stretchwas the increase of the late duration of the APs. The modelingpart of the study demonstrates that both affinity change of theTnC and activation of the SA channel current are needed toreproduce these effects seen in experiments. The model alsosuggests that SA channels do not directly modulate thefunction of the myocytes but instead increase the SR calciumstores, causing greater release of Ca21 during systole. Abigger Ca21 transient modulates the membrane voltage during

Figure 11. Comparison of modeled train of APs (A), Ca21 tran-sients (B), and APD at 90% repolarization level (C) when thestretch was simulated by increased TnC affinity and increasedSA current density.

Figure 12. The model predictions of the more severe (possiblypathophysiological) stretch on the RP (A) and the diastolic freeCa21 (B). The numbers in parentheses refer to the estimation ofthe SA current density and affinity change of the TnC given inFigure 1.

Figure 13. Detailed model predictions of the effects of increas-ing stretch on the crucial cellular functions. The curves corre-spond to the estimation of the SA current density and affinitychange of the TnC as shown in Figures 1 and 12. 1, minimumstretch; 5, maximum stretch. A, EAP denotes an early afterde-polarization; B, Ca21 transient; C, L-type calcium current; D,Na1/Ca21-exchanger current. Observe the different time scale inpanel C.



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APs through increased Na1/Ca21-exchanger inward current.The same mechanisms can also induce arrhythmogenic after-potentials, a rise in diastolic [Ca21]i, and depolarization of theRP when high enough amounts of SA channels are activatedin the model.

Properties of the ModelA mathematical model based on the Luo-Rudy model30–32wasused to support the experimental study of the stretch-dependent mechanisms. The model could reproduce thephenomena as observed in the experiments. First, it has to beclarified to what extent the model reflects the function of thecardiac myocytes. It is clear that a model cannot posses all thecomponents in the real cells, since many of them are notknown in detail presently. Despite the scarcity of facts, wehave tried to obtain as holistic point of view as possible in thedevelopment of the model. Therefore, the validity of themodel could be judged by how well it can reproducedocumented physiological behavior. Our model can producefairly similar APs as recorded from rat atrial myocytes, whichare also modulated by calcium transients in the model.Because we wanted to study the Ca21 balance of the myocytesduring stretch, the model parameters relevant to the Ca21

handling are essential. In modeling the calcium-inducedcalcium release (CICR), it has usually been assumed thatthere is only 1 cytosolic pool of calcium, the concentration ofwhich controls the release of calcium from the SR. To thispool, calcium enters from both the SR and sarcolemmalcalcium current.45 The CICR model we used is a commonpool model with 2 different release sites. The release from thefirst compartment is controlled by the L-type current, whereasthe release from the second compartment is controlled by therelease from the first compartment (see Materials and Meth-ods and Appendix for details). In this respect, our modeldiffers from all the other models used previously to study thestretch-dependent changes in the cardiac myocytes. Thewell-documented role of TnC in the stretch-dependentchanges of the heart muscle11,12 has been previously modeledto evaluate TnC-induced changes during stretch by severalauthors.13–15,46 The works by Landesberg and Sideman,13,14

Landesberg,15 and Katsnelson and Markhasin46 have thor-oughly investigated, by modeling, the role and function of thelength-dependent changes in the contractile apparatus, includ-ing increase of calcium affinity and reduction of the doublethin-filament overlap. Their results show similar changes inthe [Ca21]i, as in our work. In contrast to those works, wewanted to investigate the [Ca21]i in terms of time-dependentchanges in the function of the myocytes, including the APs,Ca21 transients, and membrane currents. Although in themodeling we had to approximate the TnC affinity changeduring stretch, our model produced changes very similar tothose observed in the experiments. The SA channel formal-ism used in our model is similar to what has been usedbefore.38

[Ca21]i During StretchA considerable agreement exists that mechanical stimulationcan influence the [Ca21]i of the myocytes. The length increaseproduces a gradual increase in Ca21 transient amplitude in

isolated cardiac preparations10 and also in isolated rat cardiacmyocytes.47 The results concerning the change of the diastolic[Ca21]i are somewhat controversial. Some studies show aclear increase in diastolic [Ca21]i,48–50 but others indicate thatcardiac myocytes can maintain constant diastolic calciumconcentration during stretch.47 Concerning systolic [Ca21],Allen et al2 suggested that augmentation of the Ca21 transientsduring stretch might be due to a change in diastolic [Ca21]i.Other studies indicate that Ca21 transients are augmentedwithout a change in diastolic [Ca21]i in isolated rat myo-cytes.47 This was also the finding in isolated rat atria in thepresent study. On the other hand, the development of theincrease of the amplitude of the Ca21 transients over a periodof several minutes10 indicates that even small changes indiastolic calcium concentration might contribute to thesechanges. The fluorescent Ca21 indicators have relatively highKd values when compared with the low [Ca21]i duringdiastole. This suggests that small changes in diastolic [Ca21]i

are hard to detect with these indicators. In general, a promi-nent rise in diastolic calcium concentration in heart myocytesindicates that Ca21 buffers are unable to remove or bind thecalcium. This is known to happen in several pathologicalsituations such as ischemia,51 in which the Ca21 buffers of thecell are incapacitated. Usually this leads to a Ca21 overload,causing abnormal electrical and contractile behavior of thetissue. It is clear that stretch can be severe enough to bepathological and cause the calcium overload. However, a risein diastolic Ca21 concentration may lead also to an increase inresting tension of the tissue that may reduce stretch of the cellmembrane. The present study shows, experimentally, that asmall amount of stretch increases the amplitude of the Ca21

transients without any detectable change in diastolic calciumconcentration. Our model simulations support the idea, sincethey can reproduce significant increase in Ca21 transientswithout prominent change in diastolic [Ca21]i.

Role of TnCThe calcium-binding part of the contractile machinery, theTnC,52 is known to be sensitive to muscle length.11,12 Inaddition to biochemical studies, many physiologically ori-ented reports suggest the prominent role of TnC in thelength-dependent activation of the cardiac tissue of differentspecies.4,5,10,53–55 If Ca21 sensitivity of TnC increases withstretch, this might influence the function of the myocytes inseveral ways, as follows. First, fast increase of the affinitywould increase the contraction force and decrease the systolic[Ca21]i. Secondly, the decay of the Ca21 transients duringstretch would be faster than what would be expected on thebasis of enzyme kinetics alone, as previously demonstrated,56

because the calcium binding “eats into” the calcium transient.Thirdly, the affinity change would favor the formation of theTnC-Ca21 complex, leading to a slower off-rate of thecomplex, and so the time course of the contraction would beprolonged. Our experimental data demonstrate that stretchdecreases the decay of the calcium transients significantly,and the model simulation shows that TnC affinity increase,alone or in combination with SA channel activation, leads tosimilar changes (Figures 7 and 9). The decline of the Ca21

transients immediately after the onset of stretch was not seen



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in the experiments, suggesting that a rise in systolic [Ca21]i

and increased TnC affinity are smoothly graded. However, inthe model, a transient decrease of the amplitude of the Ca21

transients was produced when the TnC affinity was increased(Figure 7). According to our results, the TnC sensitivityincrease contributes to the stretch-induced changes by pro-viding an additional buffering of the Ca21 ions during stretch.Increased buffering by TnC leads to an increase of thecontraction force during systole, most prominently mani-fested during the fast increase in contraction force followingstretch. During diastole this mechanism would balance the[Ca21]i or even slightly lower the diastolic [Ca21]i.

Role of SA ChannelsStretch-induced changes in heart function might be possibleto explain by SA ion channels located in the plasmalemma ofcardiac myocytes. These channels have been described, andtheir open probability has been found to depend on mechan-ical stress of the membrane.57 After the initial discovery of SAchannels,16 several types of SA channels have been docu-mented in isolated adult cardiocytes17,18,21 and in culturedneonatal cardiocytes.19,20,22 The majority of SA channelsseems to be of a type with considerable permeability to bothmonovalent and divalent cations.58 In isolated myocytesmechanical loading increases intracellular Ca21 concentra-tion,3 and interestingly, this increase can be inhibited bygadolinium (Gd31),59 a blocker of SA channels.23 Our modelreproduced a gradual increase of the calcium transients onlywhen an additional calcium influx through plasma membranewas activated. The SA channel we used in our model has apermeability ratio of 1:1:1 for Na1:Ca21:K1, similar to whathas been reported earlier from rat atrial myocytes.19 Activa-tion of the SA channel leads to an increase in [Ca21]i by directCa21 influx. Since the SA channel is permeable to Na1,increased sodium leads to the activation of the Na1/Ca21

exchanger and to an additional accumulation of Ca21 ions intothe cell. The increased [Ca21]i is pumped to the SR by theCa21 pump.60 Increased amount of calcium in SR causes agreater release of Ca21 during systole. In this scheme,potassium ions may serve as a countercurrent mechanism thatstabilizes the membrane potential during diastole. Our studydoes not rule out the possibility that the additional calciumflux comes via channels or exchangers other than the SAchannels. Since the stretch-dependent increase of the contrac-tion force in the heart muscle preparations9 and even isolatedcells61 has 2 distinct components (fast part and slow part), onehas to consider the [Ca21]i changes as a 2-step process. If theTnC affinity change and the overlap of the actin and myosinfilaments are responsible for the fast part as previouslysuggested, the additional activation of Ca21 flux wouldcontribute to the slow part by modulating the [Ca21]i of thecells. In fact, as shown in Figure 6, the increase of thecontraction force after stretch seems to consist of the 2components, increased TnC affinity and increase of the Ca21

transients, of which the latter is much slower than the former.

Role of SRCICR in cardiac myocytes can be modulated by the trigger,the L-type current through membrane, or by the release of the

Ca21 from SR. On the basis of our results, the amount of thetrigger current is not significantly changed by stretch. Thisleads to the conclusion that the Ca21 transient augmentation ismediated by the release of the Ca21 from the SR. It has beenreported that SR calcium content is increased slowly after astep increase of cardiac muscle length.62 Our model producedan increase in SR content concomitantly with the augmenta-tion of the Ca21 transient amplitude when SA channels wereintroduced to the model cell (Figure 10). However, SRcalcium content increased only 12.2%, whereas amplitude ofcalcium transients increased 20.2%, indicating a nonlinearcorrelation between SR calcium content and the amount ofcalcium released during systole. The reason for this isprobably the positive feedback in CICR,63 caused by the factthat with a higher amount of calcium in SR a biggerproportion is released during systole.64 On the premise thatour model, which has simpler Ca21 dynamics than the realcells, can reproduce this effect, we can assume that thispositive feedback is a fundamental feature of the CICR. Onthe basis of our experimental and modeling data, we canconclude that during the normal stretch-dependent activationin rat atrium, the SR has a crucial role in augmentation of theCa21 transients.

Electrical Activity of the Myocyte During StretchSince calcium transient modulates the AP65 and vice versa,66

the changes in [Ca21]i during stretch should change the shapeof the APs of the myocytes. It is known that inotropicinterventions, such as stretch, increase the late duration of theAPs67 in cardiac myocytes with a short plateau.68,69 Thishappens apparently via the increased Na1/Ca21-exchangerinward current that is boosted by augmentation of the calciumtransients.65 In rat myocytes, the Na1/Ca21-exchanger currentis proportional to [Ca21]i.

70 The present study demonstratesthat stretch influences the APs of the rat atrial myocytes. TheAPD90% was lengthened during the slow phase of the contrac-tion development. The model simulated similar changes inAPs when the simulation included SA channel activation. Themechanism suggested by the modeling was the increasedNa1/Ca21-exchanger inward current generated by bigger Ca21

transients.71 The data support the idea that SA channels donot, during moderate stretch, directly modulate APs, butinstead, the effects are mediated by the SR through theincreased Ca21 release during systole. Many reports indicatethat stretch causes a depolarization of the RP of cardiacmyocyte.3,7,72 In the present study the RP of the myocytes wasnot significantly altered by moderate stretch, neither inexperiments nor in the model. The reason for this was thatonly a very small SA current (depolarizing current) is neededto reproduce the normal physiological time-dependentchanges in rat atrial function.

Pathological Changes Caused by StretchThe effects of stretch on the function of the heart muscle havepreviously been studied on the premise that stretch can causemany pathological phenomena.73 These effects includechanges in conduction,74 excitability,73,75 and generation ofafterpotentials.40 We show that the same mechanism thatproduces typical Frank-Starling responses during moderate



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stretch in the rat atrium can also induce pathological changesin cardiac myocytes when they are subjected to a moreintense stretch. These effects were manifested in our model asdepolarization of the RP and increase of the diastolic [Ca21]i.During the stretch-induced Ca21 overload, the Ca21-inducedinactivation of the L-type Ca21 current opens a time windowin which the increased Na1/Ca21 current can trigger earlyafterpotentials.

Appendix

The Mathematical Model of the RatAtrial MyocyteThe mathematical model we used is a further development of the oneby Luo and Rudy.30–32Like their model, it includes the ionic currentsresponsible for generation of the AP (Na1, K1, and Ca21) and theNa1/Ca21-exchanger current. It also includes the Ca21 release mech-anisms and intracellular buffers. The model has been built withMATLAB software in a UNIX workstation and uses the optimizedintegration algorithms therein to solve numerically the resultingmultiple differential equations. The integration algorithm used tosolve the differential equations was based on hybrid methods.76,77Anadaptive time step was used to shorten calculation times from 500 to10 ms. Before any interventions or observations, the model wasallowed to run until a steady state was reached.

A full description of the model is beyond the scope of this paper,but certain crucial modifications as compared with the Luo-Rudymodel have to be recapitulated. The cell geometry has been changedto correspond to that of the rat atrial myocytes, including cell sizeand the size of the SR compartment. Ionic concentrations have beenmodified to be the same as those used in our experimental work.Concerning the ionic currents, the only current that has beenfundamentally changed is the K1 current, which has been modeledwith 2 time- and voltage-dependent currents (based on fast and slowinactivating channels) and 1 time-independent (noninactivating)current. The Ca21 balance has been modeled using the knowledgethat in rat about 90% of the calcium transient comes from theintracellular stores (SR), and only about 10% comes directly viaL-type Ca21 channels. The calcium release from the stores alsoincludes 2 phases, the first directly coupled to the L-type Ca21

current (release from the junctional SR) and the second triggered bythis initial release from neighboring (nonjunctional or network) SR.

The Depolarization-Activated Outward CurrentThe depolarization-activated outward current (Iout) was the mainrepolarization-inducing current. The subtypes of the outward currenthave been described in detail previously.78 In our model, theIout ismodeled with 3 components, the rapidly inactivating (Ik,fast), slowlyinactivating (Ik,slow), and nonactivating (Ik,ss) K1 current. We adaptedthe values of forward and reverse activation rate constants given byBoyle and Nerbonne78 and VanWagoner et al79 with the MATHCADmodeling tool to get the activation and inactivation into the formatused in H-H–type formulae. TheIout is given according to the H-Hmodel, as follows:

(2) I k,fast5kfastGmGacGina,fast~V2Ek!

I k,slow5kslowGmGacGina,slow~V2Ek!

I k,ss5kssGmGac~V2Ek!

whereGm is the maximum conductance ofIout, Gact is activation gate,Gina,fastis inactivation gate forIk,fast, andGina,slow is inactivation gate forIk,slow; kfast, kslow, and kss are fractional for Ik,fast, Ik,slow, and Ik,ss,respectively. Please note that the first-order kinetics of the openinggate was used instead of the fourth order,78 since the duration of APgenerated by using the fourth-order power did not match theexperimental data.

Parameter DetailsCell geometry (largely after Schaper et al80):

Cell volume:Vcell512310–6 mLSR volume:Vsr5Vcell30.1JSR volume:Vjsr5Vsr30.02NSR volume:Vnsr5Vsr30.98Capacitive membrane area:Acap50.7310–4 cm2

Extracellular ionic concentrations used:[K] o55.9 mmol/L[Na]o5131 mmol/L[Ca]o52.5 mmol/L

[Ca21]i:Calcium release from second release compartment:ton540 ms;

toff510 msThe trigger threshold of calcium release from second compartment

is half of the calcium release from first release compartmentThe time delay of second calcium release compartment is 5 msFirst calcium release compartment: maximum conductance,

Grel56 ms–1

Second calcium release compartment: maximum conductance,Grel50.046 ms–1

Ca21 pump in SR:Km.up50.46 mmol/LL-type Ca21 channel:

Pca51.62310–4 cm/sKm,ca50.27 mmol/L

Voltage-dependent outward currentIout:Maximum conductance:GK50.154=(Ko /5.4)

Voltage-independent K1 current:Maximum conductance:GK50.382=(Ko /5.4)

Initial values:Ki5140 mmol/L; Nai5131.4 mmol/L; Cai50.07 mmol/LCajsr51.73 mmol/L; Cansr51.73 mmol/L;Vo5282.1 mV

Pacing stimulus:Intensity5280 mA/mFDuration50.5 ms

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Pasi Tavi, Chunlei Han and Matti WeckströmIncreased Troponin C Affinity and Stretch-Activated Ion Channels

in Rat Atrial Myocytes : Role ofi]2+Mechanisms of Stretch-Induced Changes in [Ca

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