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Progress in Biophysics and Molecular Biology 107 (2011) 81e89

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Progress in Biophysics and Molecular Biology

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Review

Contribution of mechanical factors to arrhythmogenesis in calcium overloadedcardiomyocytes: Model predictions and experiments

Leonid B. Katsnelson a,b,*, Olga Solovyova a,b, Alexander Balakin a, Oleg Lookin a, Pavel Konovalov a,Yuri Protsenko a, Tatiana Sulman a,b, Vladimir S. Markhasin a,b

a Institute of Immunology and Physiology, Ural Branch of the Russian Academy of Sciences, 106 Pervomayskaya str, Ekaterinburg 620049, Russian FederationbUral Federal University, 19 Mira str, Ekaterinburg 620002, Russian Federation

a r t i c l e i n f o

Article history:Available online 15 June 2011

Keywords:Myocardium mechanicsHeart rhythmExtrasystoleMechanoeelectric coupling

* Corresponding author. Institute of Immunology anthe Russian Academy of Sciences, Bldg. 91, PervomayskRussian Federation. Tel.: þ7 343 3623465; fax: þ7 34

E-mail address: l.katsnelson@iip.uran.ru (L.B. Kats

0079-6107/$ e see front matter � 2011 Elsevier Ltd.doi:10.1016/j.pbiomolbio.2011.06.001

a b s t r a c t

It is well-known that Ca2þ overload in cardiomyocytes may underlie arrhythmias. However, the possiblecontribution of mechanical factors to rhythm disturbances in Ca2þ overloaded myocytes has not beensufficiently investigated. We used a mathematical model of the electrical and mechanical activity ofcardiomyocytes to reveal an essential role of the mechanisms of cardiac mechanoeelectric feedback inarrhythmogenesis in Ca2þ overloaded myocardium. In the model, the following mechanical factorsincreased Ca2þ overload in contracting cardiomyocytes and promoted rhythm disturbances: i) a decreasein the mechanical load for afterloaded contractions; and ii) a decrease in the initial length of sarcomeresfor isometric twitches. In exact accordance with the model predictions, in experiments on papillarymuscles from the right ventricle of guinea pigs with Ca2þ overloaded cardiomyocytes (using 0.5e1 mM ofouabain), we found that emergence of rhythm disturbances and extrasystoles depends on the mechanicalconditions of muscle contraction.

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Contents

1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 812. Materials and methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

2.1. Experimental methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 822.2. Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

3. Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 823.1. Model predictions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 823.2. Experiments on cardiac muscle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86

4. Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 875. Editors’ Note . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88

Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88

1. Introduction

It is well-known that Ca2þ overloading of cardiomyocytes is oftenaccompanied by rhythm disturbances (Kihara and Morgan, 1991;

d Physiology, Ural Branch ofaya str, Ekaterinburg 620041,3 3740070.nelson).

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Thandroyen et al., 1991) and may underlie heart failure. Specifi-cally, Ca2þ overload may be induced by an attenuation of theNaþeKþ pump (NKP) followed by an increase in the intracellular Naþ

concentration ([Naþ]i) and an amplification of NaþeCa2þ exchange(NCX) current (Bers, 2001). Practically, arrhythmogenic Ca2þ over-load via NKP depression may result from a glycoside treatment usedfor chronic heart failure (von Lewinski et al., 2007). Possible impli-cations of Ca2þ overloading in arrhythmogenesis, particularlyinduced by a depression of the NKP, were analyzed using mathe-matical models (Luo and Rudy, 1994; Noble and Varghese, 1998).

L.B. Katsnelson et al. / Progress in Biophysics and Molecular Biology 107 (2011) 81e8982

Noble and Varghese predictedmechanisms of spontaneous electricalactivity in response to the almost complete suppression (94%) of theNKP, using a mathematical model of cardiomyocyte electrophysi-ology (Noble and Varghese, 1998). Utilizing our integrative model ofthe electroemechanical coupling in guinea pig cardiomyocytes (seeSec. 2.2), we recently uncovered that even moderate reduction ofNKP activity may cause rhythm disturbances owing to the mecha-nisms of intracellular cardiac mechano-Ca2þ and mechanoeelec-trical coupling (Sulman et al., 2008).

Moreover, we showed that a decrease in the end-diastolicsarcomere length and a decrease in the mechanical load for car-diomyocytes may facilitate Ca2þ overloading and contribute toarrhythmogenesis and mechanical dysfunction. A short summaryof these model predictions is presented in Sec. 3.1, below.

To test the model’s predictions, we performed an experimentalstudy of the role of the mechanical conditions in the emergence ofthe electrical andmechanical disturbances. Experiments were doneon guinea pig right ventricular papillary muscles exposed toouabain, which inhibits the NKP. The experimental data agree wellwith the modeling results (Sec. 3.2). However, multicellular prep-arations of rat myocardium exposed to the same experimentalconditions and even higher ouabain concentrations did notproduce spontaneous activity. We developed a novel model of theelectromechanical activity of rat cardiomyocyte based on ouroriginal equations for mechanics (see Sec. 2.2), as in the guinea pigmodel (Sulman et al., 2008), and analyzed the species differences inthe response to NKP inhibition (see Sec. Discussion).

2. Materials and methods

2.1. Experimental methods

Animals (guinea pigs, age 1e4 months, weight 150e350 g) weretreated according to the Principles of the Care and Use of Labora-tory Animals approved by the Animal Welfare Committee of theInstitute of Immunology and Physiology. Animals were killed bycervical dislocation. The heart was quickly excised and placed intoa preparation cuvette with 30 mM BDM. A thin papillary musclewas dissected from the right ventricle. Saline solution contained (inmM) 118.5 NaCl, 4.2 KCl, 1.2 MgSO4, 2.5 CaCl2, 11.1 D-(þ)-glucose,and was perfused with 95%O2e5%CO2, pH adjusted to 7.3 withNaHCO3 and KH2PO4. The muscle was fixed to the rods of lengthservomotor and force transducer in the perfusion chamber.

Action potential (AP) in the papillary muscle cardiomyocyteswas recorded using free-floating microelectrode technique viaIntracellular Electrometer IE-210 (Warner Instruments Corp.). Freeintracellular Ca2þ (Ca2þ transient) was monitored with fluorescentdye Fura-2/AM (5 mM (Fluka Biochemika) þ 5% w/v Pluronic F-127)within a Muscle Research System (Scientific Instruments GmbH)equipped with epifluorescent inverted microscope Axiovert-200(Carl Zeiss). Either AP or fluorescent measurements were donesimultaneously with the mechanical activity of a muscle (time-dependent changes in the force and length) during contractions.The force, length, membrane potential and fluorescence lightsignals were sampled at 10 kHz by analog-to-digital (A/D) and D/Adata converter PCI-1716S (AdLink Technology Inc.) using self-madesoftware that runs under HyperKernel (ArcSystems Ltd.) real-timeintegrated environment. Chemicals were from SigmaeAldrich.

The measurements presented here were done at 30 �C. Ouabain,an NKP inhibitor, was added to the saline solution at concentrationsof 0.1e1.0 mM to promote Ca2þ overload in cardiomyocytes. Most ofthe measurements were done at a reference muscle length of0.85 LMAX (LMAX is the muscle length where the maximal isometricforce is generated). Pacing rate was varied from 0.5 Hz up to 3.0 Hz,depending on the preparation, to approach arrhythmogenic

threshold. Additional mechanical interventions were applied tomodulate Ca2þ loading, and to suppress or rebuild spontaneousactivity. Muscle length was varied from 0.85 up to 0.95 LMAX forisometric mode of contractions, and contraction mode was changedfrom isometric to auxotonic with a preset dynamic length change(shortening and relengthening) during every cycle, or the musclewas allowed to contract under small constant afterloads.

2.2. Modeling

We developed an “EkaterinburgeOxford” mathematical model(EO model) (Sulman et al., 2008) based on an electrophysiologicalmodel of the guinea pig cardiomyocyte (Noble et al., 1998) anda model of the myocardium mechanical activity developed by uspreviously (Katsnelson et al., 2004). The integrative model (a virtualmuscle sample) simulates the electrical and mechanical activity ofcardiomyocytes during isometric and afterloaded twitches underdifferent cardiomyocyte lengths and mechanical loads, as well asa wide range of the effects of cardiac mechanoemechanical,mechano-Ca2þ and mechanoeelectric feedback (Solovyova et al.,2003). A key feature of the models is inclusion of the cooperativemechanisms of Ca2þ activation of the thin filament and crossbridge(Xb) binding (Moss et al., 2004). Particularly, the Xb-induced increasein the affinity of troponin C (TnC) for Ca2þ (XbeCaTnC co-operativity)is implemented as a decrease in the dissociation rate of Ca2þ fromTnC with an increase in the amount of neighboring force-generatingXb (Izakov et al., 1991). We showed the XbeCaTnC co-operativity tobe the keymechanismwithin themodel and avital contributor to theeffects of cardiac excitationeCa2þ-contraction coupling, includingthe effects addressed in this paper ((Izakov et al., 1991; Solovyovaet al., 2003; Sulman et al., 2008), see also “Results” below).

In addition to guinea pig, parameters of the EO model were alsofitted to reproduce species-specific features of the electrome-chanical activity in rabbit cardiomyocytes (not shown). This modelwas not applicable for the analysis of experimental data which weobtained in rat myocardial preparations. This impelled us todevelop a novel model of the rat cardiomyocyte. Similar to theintegrative model of cellular electromechanics in rat myocardiumdeveloped by Niederer and Smith (Niederer and Smith, 2007), weutilized an electrophysiological model of the rat cardiomyocyte(Pandit et al., 2001) coupled with a model of intracellular Ca2þ

handling (excepting the equation for CaTnC kinetics) (Hinch et al.,2004). Unlike the mechanical part of the Niederer and Smithmodel (Niederer and Smith, 2007), we used our original equationsfor the mechanical activity and CaTnC kinetics (Katsnelson et al.,2004). This new integrative model simulates a wide range ofexperimental data obtained in rat myocardial preparations, andparticularly isometric and afterloaded contractions of rat papillarymuscle at the pacing rates of 0.3e3.0 Hz (see Fig. 1, right top panel).

3. Results

3.1. Model predictions

Our model of the guinea pig cardiomyocyte produces simulta-neous disturbances in both the electrical and mechanical activity asthe result of a moderate inhibition of NKP activity (Sulman et al.,2008). Modeling results are shown in Figs. 1e4 and 6. The NKPdecrease causes Ca2þ overload in cardiomyocytes, following anincrease in [Naþ]i and an amplification of the reverse mode of NCXcurrent (Fig. 1, left). The rhythm disturbances and extrasystoles aretriggered by spontaneous APs induced by activation of the inwardNCX current following spontaneous Ca2þ releases from the over-loaded SR between regular stimuli (Figs. 2A, 4 and 6, left panels).Note that the SR Ca2þ overload is progressively evaluated during

Fig. 1. Comparison between the effects of NKP inhibition (the same reduction of the Naþ-binding Michaelis constant for NKP, Km,Na ¼ 40 mM) in the guinea pig (left panels) and rat(right panels) cardiomyocyte models. Virtual sample length in each case is 0.90 LMAX. Top row: superposition of the force (black) and action potential (gray) (arbitrary units for both),in a single isometric twitch showing much shorter AP and faster force generation in rat than in guinea pig. Consequent rows show cycle-by-cycle changes in the isometric force(arbitrary units), Ca2þ concentration in the junctional SR ([Ca2þ]SR), and [Naþ]i in response to an increase in pacing rate from 1.0 Hz (prior the time shown in the panels) to 1.25 Hz.In the guinea pig model, a significant Ca2þ overload of the SR triggers spontaneous activity. The rat model demonstrates moderate SR Ca2þ accumulation that does not approach thethreshold for spontaneous releases, even over an extended period of time.

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period of spontaneous activity of the muscle (see Figs. 1 and 3 forCa2þ concentration in the junctional SR) due to extra Ca2þ entry viaL-type Ca2þ currents activated by spontaneous APs. Moreover, iftime delays between interchanging spontaneous and electricallystimulated APs are rather short, the APs mostly induce decreasedCa2þ releases and depressed Ca2þ transients (see Fig. 4 for Ca2þ

transients). Thus corresponding L-type Ca2þ currents may be lessinactivated by cytosolic Ca2þ (Bers, 2001), that may additionallycontribute to the Ca2þ overload self-maintenance.

Note that rhythm disturbances secondary to the moderate NKPinhibition occurred in the model at pacing rates of 1 Hz and above.

We found that XbeCaTnC co-operativity plays a significant role inthe generation of spontaneous Ca2þ releases in Ca2þ overloaded cells(Sulman et al., 2008). Briefly, during the relaxation phase of everyregular twitch, Ca2þ release from TnC intensifies regeneratively (adecrease in the number of force-generating Xb accelerates CaTnCdissociation). In Ca2þ overloaded cardiomyocytes this leads to theappearance of a minor elevation (a “hump”) of cytosolic [Ca2þ]iduring the late phase of relaxation (Fig. 2A), which the NCX is inca-pable of smoothing (unlike the normal cells). This increase is suffi-cient to initiate spontaneous Ca2þ-induced Ca2þ release (CICR) fromthe overloaded SR and trigger subsequent extrasystole (Fig. 2A).

To confirm directly the key role of the XbeCaTnC co-operativity,we switched off this mechanism in the model from the onset of the

relaxation phase by fixing the CaTnC off-rate constant from theinstant and thus eliminating further effects of the Xb-kinetics onCaTnC dissociation (Fig. 2B and C, showing the difference in thetime course of CaTnC off-rates). An extrasystole that developed inthe model with the XbeCaTnC co-operativity (Fig. 2A) vanisheddue to the co-operativity exclusion (Fig. 2B).

Moreover, we found that a decrease in either the initial sarco-mere length or in the mechanical load may facilitate arrhythmo-genesis via the same XbeCaTnC co-operativity mechanism, whenthe NKP activity is reduced (Sulman et al., 2008). We found a borderzone of moderate NKP attenuation (with the Naþ-bindingMichaelisconstant Km,Na in a narrow range of 37e40 mM) that separatedarrhythmogenic (Km,Na� 40 mM) and normal (Km,Na < 37 mM) NKPstate (Sulman et al., 2008). In this border zone the model mayexhibit either normal stable contractions or rhythm disturbancesdepending on the cardiomyocyte length (Sulman et al., 2008) andthe mechanical load (Figs. 3 and 4). We called virtual musclesamples with Km,Na from the border zone Sub-Critical (SC) samples.It turned out that the smaller the initial sarcomere length ormechanical load, the earlier the SC sample undergoes extrasystoles(see Fig. 3 here, and also Fig. 8 in our previous work (Sulman et al.,2008) showing spontaneous activity arising in the SC sample in theseries of isometric contractions at different lengths from 0.82 LMAXto 0.90 LMAX).

Fig. 3. Mechanical load-dependence of the spontaneous activity in a sub-critical (SC) virtual muscle sample (Km,Na ¼ 38 mM, see text for details). Contractions of the SC sample areshown in isometric mode (left), and under afterloads of 0.6 F0 and 0.2 F0 (middle and right). F0 is the peak force developed during the first isometric contraction of the series. A fixedreference sarcomere length (Lref ¼ 0.90 LMAx) is set for the isometric contractions and used as the initial sarcomere length in all the afterloaded contractions at pacing rate of 1.25 Hz.From top to bottom: the curves show beat-to-beat envelope lines traced through the peak force, shortest sarcomere length (as % of Lref), and diastolic Ca2þ concentration in thejunctional SR ([Ca2þ]SR, dotted lines show the curve at the isometric mode) during consequent contractions. Rhythm disturbances did not arise at afterloads �0.7 F0, but did emergeat afterloads �0.6 F0. The smaller the afterload, the earlier rhythm disturbances appeared.

Fig. 2. Effect of the XbeCaTnC co-operativity on the extrasystole generation. A) The regular and extrasystolic contractions are magnified from Fig. 1, left panel, 137e138 s. Top tobottom: time course of the tension development (F, arbitrary units), calcium transients ([Ca2þ]i) and membrane potential (E) are shown. Scores under the graph indicate the regularstimuli (each 0.8 s), (*) indicates an extra AP following the regular one. B) The extra AP and extrasystole vanished in the model with the XbeCaTnC co-operativity excluded duringthe relaxation phase from an instant indicated by the empty arrow. C) The time-dependent Ca2þ off-fluxes from TnC(CaTnC off-rate) for the contractions from the panels A (solidline) and B (dotted line) are shown. A small “hump” on the solid line results from a cooperative increase in the CaTnC dissociation rate due to a decrease in the number of force-generating Xbs during the late relaxation phase. The difference between off-rates being integrated contributes to the “hump” in [Ca2þ]i on the panel A, that is sufficient to initiatespontaneous Ca2þ-induced Ca2þ release from the overloaded SR and trigger subsequent extra AP and extrasystole.

L.B. Katsnelson et al. / Progress in Biophysics and Molecular Biology 107 (2011) 81e8984

Fig. 4. Detailed view of the spontaneous activity in an SC sample during afterloaded contractions. Top to bottom: time course of the force (F), sample length (L), Ca2þ transients([Ca2þ]i) and membrane potential (E) in the SC sample shown in Fig. 3 (central panel) at the afterload of 0.6 F0 during the time interval from 210 to 242 s. Time scale marks indicatethe regular stimuli (every 0.8 s). Spontaneous Ca2þ releases from the SR induce rhythm disturbances and the force falls below the afterload level, which causes the loss ofshortenings and a final collapse.

L.B. Katsnelson et al. / Progress in Biophysics and Molecular Biology 107 (2011) 81e89 85

The contractile ability of a virtual muscle sample overloadedwith Ca2þ (i.e. ability to produce force and shortening) was signif-icantly reduced after an extrasystolic attack. In cases shown inFigs. 3 and 4, the SC sample could not shorten after the extrasystolicattacks, because its developed force has fallen below the afterloadvalue. In a number of cases, sustained force alternance occurredafter the phase of spontaneous activity (Sulman et al., 2008). Asa whole, the sudden disturbances in cardiac electrical andcontractile activity as demonstrated in Figs. 1 (left), 3 and 4resemble the events observed in patients developing acute heartfailure.

Fig. 5. Spontaneous activity in a guinea pig papillary muscle with Ca2þ overloaded cardiomyseries of isometric twitches at a fixed muscle length of 0.85 LMAX is shown. An increase in pacof the peak force followed by the slow monotonous force decrease and finally resulted in thonset). Black dots indicate regular stimuli. In regular twitches the dots are lying on the basabove the diastolic baseline show those regular stimuli which occur in the time course of prithe guinea pig model simulations (see Fig. 1, left panels). B) Time-dependent isometric forcmuscle at muscle length of 0.85 LMAX, 2 Hz pacing rate, showing the onset of spontaneous

Earlier, we used the model to uncover a mechanism for thecontribution of mechanical conditions of contraction to arrhythmiainmoderately Ca2þ overloaded cardiomyocytes (Sulman et al., 2008).It is as follows: a decrease in the initial sarcomere length or addi-tional sarcomere shortening under low afterloads leads to theadditional Ca2þ releases from TnC due to the length dependence ofthe XbeCaTnC co-operativity during every contractionerelaxationcycle. This modulates the cytosolic Ca2þ transient that, in turn,slightly amplifies Ca2þ uptake from the cytosol by the SERCA Ca2þ

pump versus Ca2þ outflow through the forward mode of NCX.Therefore, during every contractionerelaxation cycle somewhat

ocytes (1 mM ouabain) resulting from an increase in pacing rate. A) The time-dependenting rate (here from 1 Hz to 2.5 Hz as indicated in the top bars) caused the transient risee emergence of the rhythm disturbances (black arrow shows the spontaneous activityeline of the active force indicating the onset of consequent contraction. The dots lyingor extrasystolic contraction. Compare the experimental result with a similar example ofe (top) and Fura-2/AM light intensity (bottom) are registered in a guinea pig papillaryactivity.

Fig. 6. Spontaneous APs and extrasystoles generated in a virtual guinea pig muscle sample (a zoomed-in fragment from Fig. 1, left panel) and in a guinea pig papillary muscle (azoom view from Fig. 5A) during the period of sustained spontaneous activity. Time-dependent changes in the isometric force and membrane potential (E) are shown. Black dotsindicate regular pacing. A) Spontaneous APs appear in between regular stimuli as distinct ones. B) The onset of spontaneous AP occurs shortly before the regular stimuli, so the latterfalls on the repolarization phase for the spontaneous AP and produces abortive AP.

L.B. Katsnelson et al. / Progress in Biophysics and Molecular Biology 107 (2011) 81e8986

more Ca2þ is accumulated in the SR as compared to the isometriccontractions at the reference length. Thus, a decrease in either thesarcomere length or the mechanical load promotes a gradual (beat-to-beat) additional Ca2þ loading of the SR. The bottom row in Fig. 3demonstrates this additional Ca2þ accumulation during afterloadedcontractions in contrast to the control isometric conditions. Thismechanism contributes to the cell Ca2þ overloading and thus facil-itates overcoming the arrhythmogenic threshold.

3.2. Experiments on cardiac muscle

In our experiments with guinea pig papillary muscles exposed toouabain at various concentrations (0.5e1.0 mM), we registered themechanical activity along with AP or Ca2þ transients in the prepa-ration cells. Ouabain caused a gradual increase in the isometric forceof the muscle at a fixed pacing rate (1 Hz) and a constant referencemuscle length Lref set to 0.85 LMAX. The inotropic effect of ouabain

Fig. 7. The emergence of spontaneous activity in a guinea pig papillary muscle with Ca2þ ovmode of contraction (shown in the middle bars). Muscle force (top) and length (bottom) areset to 0.85 LMAX and used as the initial length in auxotonic contractions. Black dots indicextrasytolic contractions.

was the result of enhanced intracellular Ca2þ loading via decreasedNKP activity. The preparation approached steady-state contractionsat the control pacing rate, whereupon different interventions (anincrease in the pacing rate and/or changes in the mechanicalconditions of muscle contractions) were applied for an additionalmodulation of the intracellular Ca2þ level.

Spontaneous contractions occurred between stimuli in a numberof the preparations (n ¼ 22) treated with ouabain as the response toan increase in the pacing rate (Fig. 5). Representative transientprocess of the force change, sudden onset of the rhythm distur-bances and chaotic force development (demonstrated in Fig. 5A) is ingood qualitative agreement with the predictions we obtained in theframework of the cardiomyocyte model with a moderate inhibitionof the NKP (see Fig. 1, left).

In experiments where the mechanical activity was registeredsimultaneously with either AP or the changes in [Ca2þ]i, weobserved spontaneous AP and extra Ca2þ transients preceding the

erloaded cardiomyocytes (1 mM ouabain) after the change from isometric to auxotonicregistered at 1 Hz pacing rate. The reference muscle length (Lref) in isometric twitches isate regular pacing. The dots lying above the diastolic force baseline fall on the prior

Fig. 8. The influence of the mechanical conditions on the emergence of spontaneous activity in a guinea pig papillary muscle with Ca2þ overloaded cardiomyocytes (1 mM ouabain).The experimental record of the force developed in the preparation is shown. Bars on the top show the experimental protocols for changes in the pacing rate, muscle length (in % ofa reference length Lref ¼ 0.85 LMAX) fixed in isometric twitches or set as the initial length in auxotonic contractions, and contraction mode (AUX ¼ auxotonic). Black dots indicateregular pacing. Phase 1 shows a force transient after an increase in the pacing rate (from 1 Hz to 2 Hz) at the isometric mode of contractions. Phase 2 shows emergence ofextrasystoles (some dots are scattered above the diastolic force baseline, indicating regular stimuli that occur during extrasystolic contractions). Phase 3 shows the response tomuscle stretch by 7% of Lref. The frequency of extrasystoles reduces significantly from 50 extrasystoles in the first time quarter of the phase to 10 extrasystoles during the last timequarter of the phase. Phase 4 shows termination of the spontaneous activity resulting from the further increase in the preparation length up to 110% of Lref. Phase 5 shows therebuilding of the spontaneous activity shortly after the switch from isometric to auxotonic mode of contraction. Note the rise of the passive force during the record due to thepreparation stretch. This particularly resulted in a cyclic force decrease below the baseline diastolic force of the stretched preparation during the auxotonic shortening (see phase 5).

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extrasystoles (Figs. 5B and 6). These experimental recordings agreewell with the modeling results (Figs. 4 and 6). Spontaneous APsoften appeared more-or-less shortly before the subsequent regularstimuli (Fig. 6). In this case the regular stimulus induces an abortiveAP that affects the extrasystolic contraction and does not allowa regular twitch to develop (Fig. 6, right). Similar patterns of theelectrical and mechanical disturbances were predicted in thevirtual muscles as well (Fig. 6, left).

To our good fortune, we succeeded in registering the effects of thedirect mechanical interventions on the spontaneous activity inmyocardial preparations (n ¼ 4) exposed to ouabain. In accordancewith the model predictions, we observed either the termination ofthe spontaneous activity due to an increase in muscle length forisometric twitches (Fig. 8), or the emergence of rhythm disturbancesresulting from the switch from isometric to auxotonic mode ofcontractions (Figs. 7 and 8). The latterwere implemented by imposedcyclic deformations (shorteningerelengthening) of the preparationwhich resemble muscle contractions under small afterloads.

Fig. 8 demonstrates an experiment where pro- and contra-arrhythmogenic effects of several inotropic interventions, namelya change in the pacing rate, muscle stretch and switch between thecontraction modes, were registered in one and the same prepara-tion. These data also agree well with the model predictions.

4. Discussion

Possible links between mechanical conditions of contractionsand heart rhythm disturbances are still poorly understood. Thereis evidence that both myocardium strain and mechanical loadingmay affect AP generation in cardiomyocytes (Lab, 1999; Whiteet al., 1995). Mechanical interventions may induce rhythmdisturbances and even cardiac arrest (Link, 2003). Contribution ofthe mechanics to the electrical activity in myocardium is mostoften attributed to the mechano-sensitive currents (Kohl et al.,2006). Influence of the mechano-dependent kinetics of intracel-lular Ca2þ on the AP generation is much less studied and simulated(Kaufmann et al., 1971; Lab et al., 1984; Solovyova et al., 2003,2004). Here we focus on the effects of the mechanical conditionsof myocardium contraction on the arrhythmogenesis in specificpathological conditions associated with the Ca2þ overload of car-diomyocytes. In this particular case mechanisms of the mechano-Ca2þ feedback appear to play a key role as suggested from directexperimental data and model predictions (Sulman et al., 2008; terKeurs et al., 2006).

Arrhythmias caused by intracellular Ca2þ overload are well-known. They have been registered in isolated cardiomyocytes,multicellular cardiac preparations, in the whole heart, and in theclinic (Kihara and Morgan, 1991; Thandroyen et al., 1991; Zaugg,2004). However, the possible role of the mechanical factors insuch rhythm disturbances is not fully clarified.

Earlier we addressed this topic in the framework of mathe-matical modeling (Sulman et al., 2008). In particular, we found thatboth a decrease in end-diastolic sarcomere length and a decrease inthe mechanical load in Ca2þ overloaded cardiomyocytes mayincrease the risk of extrasystolic attack (Figs. 1e4, Fig. 6).

Of course, these theoretical predictions required experimentalvalidation, which is detailed in this paper (Figs. 5e8). The experi-mental results obtained in guinea pig papillary muscle witha decreased NKP activity (via ouabain exposure) confirm modelpredictions on the effects of pacing rate (Figs. 5 and 6) and of thedirect mechanical interventions on arrhythmogenesis (Figs. 7 and 8).One quantitative distinction between the modeling and experi-mental results seems to be worth discussing: the time intervalwhere multicellular muscle preparations exhibited spontaneousactivity (see e.g. Fig. 5A) appeared to be longer than predicted by themathematical cardiomyocyte model (Fig. 1, left panels). One possiblecause of this distinctionmay be the non-uniformity in Ca2þ overloadacross the papillary muscle. Furthermore, internal mechanicalheterogeneity of the multicellular preparation may also result in thedynamic shortening and/or lengthening of interacting sarcomereseven in the isometric twitches of the muscle. Perhaps, this hetero-geneity may contribute to arrhythmia prolongation, as we predictedin the model of mechanically interacting cardiomyocytes (Sulmanet al., 2008) or in the way suggested by other authors (ter Keurset al., 2006; Wakayama et al., 2005). They showed that Ca2þ wavesand following arrhythmia can reversibly be induced in muscle withnon-uniform excitationecontraction coupling due to interactionbetween the intact and damaged regions even at normal SR loading(Wakayama et al., 2005). Both separate mechanisms: proper Ca2þ

overload and non-uniformity of contraction may be linked andfacilitate arrhythmogenesis. Local spontaneous Ca2þ releases fromoverloaded SR, particularly in the muscle regions where sarcomereshortening occurs during the relaxation phase (due to the non-uniformity of contraction), may propagate in the form of Ca2þ

waves that in turn cause non-uniform contractions, thus promotingextrasystolic activity in the Ca2þ overloaded muscle.

We believe that the experimental data presented in Figs. 7 and 8convincingly demonstrate mechano-dependence of the arrhythmia

L.B. Katsnelson et al. / Progress in Biophysics and Molecular Biology 107 (2011) 81e8988

onset. Indeed, in both cases after the setting of regular isometriccontractions without extrasystoles at a fixed muscle length (atLref ¼ 0.85 LMAX in Fig. 7 or at 110% of Lref in Fig. 8) and at a fixedpacing rate (1 Hz in Fig. 7 or 2 Hz in Fig. 8), spontaneous activityarose only in response tomuscle exposure to auxotonic contractions,where the preparation undergoes cyclic shorteningerelengthening.

Note that both the model predictions and experimental datapresented here would seem to mismatch a number of other experi-mental findings and model results obtained in isolated cells, multi-cellular preparations and the whole heart, which show thatsarcomere stretch, rather than a decrease in sarcomere length,promotes spontaneous Ca2þ releases and/or autorhythmic activity inpreparations (Iribe et al., 2009; Janse et al., 2003; Kohl et al., 1999;Zabel et al., 1996). However, there are also some other experi-mental data demonstrating extra AP development in response to thequick release of the heart muscle (Hennekes et al., 1981). Arrhyth-mogenic effects of either positive or negative deformations mayresult from different intracellular mechanisms depending on themechanical conditions of contraction and specific myocardial state.Ourmodel predictions point out the key role of the length-dependentcooperative mechanisms of the cardiomyocyte Ca2þ activation intriggering extrasystoles in the case of cardiomyocyte Ca2þ overload.As shown, smaller sarcomere lengths are accompanied with highercooperative Ca2þ dissociation from TnC. Via this mechanism,a decrease in themuscle lengthmayadditionally promote theSRCa2þ

overload and thus increases the risk of arrhythmia.It is worth noting that we did not observe a slow force response

(SFR) to the stretch (Calaghan et al., 2003) in papillary musclesexposed to ouabain (see Fig. 8, phases 3 and 4). This result isconsistent with a decrease in SFR observed in failing humanmyocardium (von Lewinski et al., 2009). The model predictionssuggest that spontaneous Ca2þ releases from the overloaded SRbetween regular stimuli (even those not sufficient to induceextrasystoles, see Fig. 4 for [Ca2þ]i) may impede additional Ca2þ

accumulation underlying SFR on stretch. It allows us to speculatethat the mechanisms underlying stretch effects in myocardiummight be affected in the case of Ca2þ overload in cardiomyocytes.

In addition to the experimental data we registered in guinea pigpapillary muscles (Figs. 5e8), we have also observed similarepisodes of spontaneous activity in papillarymuscles from the rightventricle of rabbit in response to NKP inhibition (not shown). At thesame time, unexpectedly for us, we have not seen any rhythmdisturbances in papillary muscles of rat under ouabain exposure(with even much higher concentrations up to 100 mM) at the samerange of pacing rates as used for guinea pig and rabbit. To uncoverpossible mechanisms of the species-specific response to NKPinhibition, we developed a novel mathematical model of excita-tionecontraction coupling in rat cardiomyocytes (see Sec. 2.2) andsimulated NKP attenuation in the rat model, as was done in ourguinea pig model (Sulman et al., 2008).

The rat model does not produce spontaneous activity under thesame conditions (parameters of the NKP current, pacing rates, andmechanical conditions) as the guinea pig model does (see Fig. 1). Inboth models there is an essential increase in [Naþ]i, while much lessprominent Ca2þ gain occurs in the ratmodel and the arrhythmogenicthreshold is not approached (Fig.1). Themodel analysis suggests thatpeculiarities of the NCX may underlie the observed interspeciesdifferences. In agreement with experimental data (Bers et al., 1996),the NCX current, and especially Ca2þ influx via the reverse mode ofNCX, contributes essentially less to Ca2þ transient and the SR Ca2þ

loading in rat cardiomyocytes, as compared to guinea pig and rabbit.Moreover, the SR volume fraction in cardiomyocytes of guinea pig isseveral times lesser than that of rat (Bers, 2001). This species-specificratio is the feature of the respectivemodels. That iswhyguinea pig SRturned out to bemore loadedwith Ca2þ than that of rat even at equal

Ca2þ entry to the cells. These circumstances may explain rathermoderate SR Ca2þ accumulation following the increase in [Naþ]i inrat, preventing from the SR Ca2þ overload and from the heart rhythmdisturbances. Probably, in our experiments on rat papillary muscleswe did not access the critical Ca2þ SR loading before approaching thetoxic effects of ouabain. This may explain our unsuccessful attemptsto induce spontaneous activity in rat papillarymuscle by exposure toouabain versus experiments where Ca2þ overload and consequentspontaneous activity was attained in rat preparations by exposure tohigh extracellular [Ca2þ]o (Diaz et al., 1997; ter Keurs et al., 2006;Wasserstrom et al., 2010).

As mentioned above, the successful experiments where weregistered direct mechanical effects (static or dynamic perturbationsof muscle length) on the emergence of spontaneous activity inpapillary muscle were rather rare events (4 experiments out of 22registered spontaneous activity in response to ouabain and pacingrate increase).Moreover,we think that themechanical effects on Ca2þ

overloading and rhythm disturbances would probably not have beenfound at all without the guidance of the mathematical model’spredictions. Indeed, according to themodel analysis, a border zone forNKP depression that separates stable and unstable behavior of car-diomyocytes at any mechanical conditions is very narrow, and onlywithin this border zone emergence of rhythm disturbances directlydepends on the mechanics. So, we were lucky to have found theexperimental conditionswhere papillarymuscle actually exhibits thissub-critical behavior. With that, the model predictions suggestXbeCaTnC co-operativity mechanism may play an arrhythmogenicrole beyond the sub-critical range of the NKP depression. First of all, itdecreases the arrhythmogenic threshold of the SR Ca2þ load forspontaneous Ca2þ releases. Moreover, in the case of higher than sub-critical pump inhibitionwhere arrhythmogenic attack emerges at anymechanical conditions, it happens sooner with shorter sarcomerelengths and lower mechanical loads during contraction (Fig. 3).

Presented work shows a successful example of the interplaybetween experimental and computational models in studyingmechanisms of arrhythmogenesis. It demonstrates how modelpredictions may guide experimental design and new data explo-ration, while unexpected experimental data require further anal-ysis and new insights for development of mathematical models.

Editors’ Note

Please see also related communications in this issue byEvangelista et al. (2011) and May et al., (2011).

Acknowledgments

This work is supported by the Ural Branch of RAS, RBRF 10-04-00601-a, 11-04-00785-a.

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