dynamical analysis of the calcium signaling pathway in cardiac myocytes based on logarithmic...

© 2008 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim 639

Biotechnol. J. 2008, 3, 639–647 DOI 10.1002/biot.200700247 www.biotechnology-journal.com

1 Introduction

The ubiquitous second messenger Ca2+ plays thecentral role in cardiac excitation–contraction (E–C)coupling, the process in which electrical depolar-ization of the sarcolemmal membrane in cardiacmyocytes is transduced into contraction of the my-ocytes [1]. The Ca2+ dynamics of E–C coupling areprimarily regulated by the “on” reaction that intro-duces Ca2+ into the cytoplasm and the “off” reaction

through which the cytosolic Ca2+ is removed by thecombined action of the system components such asbuffers, pumps, and exchangers [2]. During the onreaction, depolarization of the sarcolemmal mem-brane opens the voltage-dependent Ca2+ channels(L-type Ca2+ channel (LTCC)) and triggers Ca2+ in-flux from the extracellular medium to the cyto-plasm. Ryanodine receptor (RyR) in the immediatevicinity of LTCC is then activated and releases alarge amount of Ca2+ from sarcoplasmic reticulum(SR) by Ca2+-induced Ca2+-release (CICR) mecha-nism [3]. The rapidly increased Ca2+ in the smalldyadic volume between LTCC and RyR diffusesthrough the cytoplasm and binds to the myofila-ment protein Troponin C, thereby switching on thecontractile machinery [1]. During the off reaction,the increased cytosolic Ca2+ gets mainly removedby SR Ca2+ pump (SERCA) and Na+/Ca2+ exchang-er (NCX), which leads to relaxation of the myocyte[2, 4, 5].

Survival of cells including cardiac myocytes re-lies on Ca2+ homeostasis – the Ca2+ flux during the

Research Article

Dynamical analysis of the calcium signaling pathway in cardiacmyocytes based on logarithmic sensitivity analysis

Tae-Hwan Kim1, Sung-Young Shin1, Sang-Mok Choo2 and Kwang-Hyun Cho1

1Department of Bio and Brain Engineering and KI for the BioCentury, Korea Advanced Institute of Science and Technology(KAIST), Daejeon, Republic of Korea

2School of Electrical Engineering, University of Ulsan, Ulsan, Republic of Korea

Many cellular functions are regulated by the Ca2+ signal which contains specific information in theform of frequency, amplitude, and duration of the oscillatory dynamics. Any alterations or dys-functions of components in the calcium signaling pathway of cardiac myocytes may lead to a di-verse range of cardiac diseases including hypertrophy and heart failure. In this study, we have in-vestigated the hidden dynamics of the intracellular Ca2+ signaling and the functional roles of itsregulatory mechanism through in silico simulations and parameter sensitivity analysis based onan experimentally verified mathematical model. It was revealed that the Ca2+ dynamics of cardiacmyocytes are determined by the balance among various system parameters. Moreover, it wasfound through the parameter sensitivity analysis that the self-oscillatory Ca2+ dynamics are mostsensitive to the Ca2+ leakage rate of the sarcolemmal membrane and the maximum rate of NCX,suggesting that these two components have dominant effects on circulating the cytosolic Ca2+.

Keywords: Calcium dynamics · Calcium signaling system · Logarithmic sensitivity analysis · Mathematical modeling · Parametersensitivity analysis

Correspondence: Professor Kwang-Hyun Cho, Department of Bio andBrain Engineering, Korea Advanced Institute of Science and Technology,335 Gwahangno, Yuseong-gu, Daejeon 305-701, Republic of KoreaE-mail: [email protected]://sbie.kaist.ac.krFax: +82-42-869-4310

Abbreviations: E–C, excitation-contraction; LSA, logarithmic sensitivityanalysis; LSF, logarithmic sensitivity function; LTCC, L-type Ca2+ channel;NCX, Na+/Ca2+ exchanger; RyR, ryanodine receptor; SR, sarcoplasmic reticulum

Received 29 November 2007Revised 18 December 2007Accepted 8 January 2008

BiotechnologyJournal Biotechnol. J. 2008, 3, 639–647

640 © 2008 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim

off reaction should exactly match that of the on re-action since cellular functions are determined andregulated by the properties of the Ca2+ dynamicssuch as frequency, amplitude, and duration [2]. Al-terations on the intracellular Ca2+ dynamics subse-quent to the dysfunction of a system componentmight lead to the altered E–C coupling followed bycardiac diseases such as hypertrophy, arrhythmias,and heart failure. The intracellular Ca2+ dynamicshave been known to be primarily controlled byLTCC, RyR, SERCA, NCX, and other slow process-es mediated by PMCA and mitochondria [6, 7].However, the dynamic regulation of the Ca2+

signaling system is not yet completely under-stood.

The aim of this paper is to elucidate the hiddendynamics of the intracellular Ca2+ regulatorymechanisms and to investigate the functional roleof the Ca2+ regulatory components through in silicosimulations and parameter sensitivity analysisbased on an experimentally verified mathematicalmodel. Our results show that the intracellular Ca2+

dynamics exhibit four different characteristics withrespect to parameter variations: faint, damped-os-cillatory, sustained-oscillatory, and diverging be-haviors. Through a logarithmic sensitivity analysis(LSA), we have revealed that the leakage rate of thesarcolemmal membrane and the maximum rate ofNCX have the most significant effects on the intra-cellular Ca2+ dynamics and the open fraction of RyR.

2 Materials and methods

2.1 The mathematical model of a calcium signalingsystem

It is being recognized that the mathematical mod-eling of cardiac myocytes is a useful tool for inves-tigating the complex biological process of electricalE–C coupling and the intracellular Ca2+ dynamics[8]. For instance, the mathematical model proposedby Bondarenko et al. [9] successfully described thesophisticated electrical phenomena of the cellmembrane and ion channels, and the intracellularCa2+ dynamics (Fig. 1). Although there are manyother mathematical models describing all the de-tails of electrical characteristics [8–11], we employin this paper a simplified but experimentally well-validated mathematical model proposed by Tangand Othmer (to be referred to as “T–O model”) [12]since our analysis focuses only on the Ca2+ dynam-ics of cardiac myocytes (Fig. 2).This model can stillexplain all the essential phenomena observed incardiac myocytes except the detailed electricalcharacteristics.

The T–O model consists of two compartments:cytoplasm and SR (Fig. 2). Since Na+ is not includ-ed in this model and the Ca2+ ATPase pump of thesarcolemmal membrane is one of the minor players[1], these two components are combined into a sin-gle NCX. The T–O model describes the followingmechanisms: the cytosolic Ca2+ is increased byLTCC, RyR, and Ca2+ leakage through the sar-colemmal and SR membranes. In contrast, it is de-creased by NCX and SERCA since NCX extrudesthe cytosolic Ca2+ to the extracellular medium andSERCA reuptakes the cytosolic Ca2+ into SR. TheSR Ca2+ gets increased by SERCA while it gets de-creased by RyR and the leakage across the SRmembrane. The SR Ca2+ release through RyR isregulated by the difference between the SR Ca2+

concentration and the cytosolic Ca2+ concentration,the RyR channel conductance, and the open prob-ability of RyR. In general, the SR Ca2+ concentra-tion is much higher than that of the cytosolic Ca2+.Hence, Ca2+ is released from SR into the cytoplasmwhen the channel opens.

RyR consists of four subunits and has two Ca2+

binding sites, one for activation and the other forinactivation. In the T–O model, four different statesof RyR are considered depending on the occupa-tion status of the two regulatory Ca2+ binding sites(Fig. 3). Here, S0 denotes the refractory state whereCa2+ is bound to the negative regulatory site, S1 in-dicates the activatable state where Ca2+ is notbound to any regulatory site, S2 denotes the openstate where Ca2+ is bound to the positive regulato-ry site, and S3 indicates the closed state where Ca2+

is bound to both sites. It is assumed that RyR opensonly at the state of S2. Hence, the open probabilityof RyR is determined by the cytosolic Ca2+.To mod-el the RyR kinetics, dimensionless state variablesare defined for the fraction of each RyR state as fol-lows:

where RT denotes the total concentration of RyR(i.e., RT = S0 + S1 + S2 + S3 and 1 = x0 +x1 + x2 + x3).

In summary, the mathematical model of the cal-cium signaling system depicted in Fig. 2 is repre-sented by the following state equations (see Table 1for the description of parameter values and the ini-tial conditions):

(1)

xt

a x a x x d d31 0 2 2 4 1 2( ) –( )= + +

dd

xx3,

ddxt

a x x d21 1 4 2= + xx d a x x3 1 2 4 2–( ) ,+

ddxt

d x d x a a x x11 2 2 0 1 2 1 4= + +–( ) ,

xSR

xSR

xSR

and xSR0

01

12

23

3= = = =T T T T

, , ,


Biotechnol. J. 2008, 3, 639–647 www.biotechnology-journal.com

Figure 1. Illustration of the intracellular Ca2+ regulatory mechanism. The regulatory system consists of four compartments: JSR, NSR, dyadic volume, andcytoplasm. The Ca2+ dynamics are regulated by potassium channels, sodium channels, calcium channels, and transporters. The ion currents and the Ca2+

fluxes depicted in this figure are as follows: IKto, the transient outward K+ current; ICa, b, the background Ca2+ current; INa, the fast Na+ current; INa, b, thebackground Na+ current; INa, Ca, the Na+/Ca2+ exchanger current; IP(Ca), the Ca2+ pump current; INa, K, the Na+/K+ pump current; IK, the delayed rectifier K+

current; IK1, the time independent K+ current; Ins(Ca), the nonspecific Ca2+ current; ICaL, the L-type Ca2+ current; Jrel, the Ca2+ flux released from SR; Jtr, theCa2+ flux transferred from NSR to JSR; Jleak, the Ca2+ leakage from SR; Jup, the Ca2+ uptake through SERCA; Jxfer, the Ca2+ flux transferred from the dyadic vol-ume to the cytosol. Among these, we focus on the following key Ca2+ current and fluxes: ICaL, Jup, Jrel, and JNaCa.

Figure 2. A schematic diagram of the simplified calcium signaling system basedon the T–O model.



where xi (i = 0, 1, 2, 3) denotes the fraction of thefour different RyR states (Fig. 3), x4 the cytosolicCa2+ concentration, x5 the Ca2+ concentration in SR,and JLTCC the Ca2+ influx through LTCC.

2.2 A logarithmic sensitivity function (LSF)

Parameter sensitivity analysis is the process of de-termining the sensitivity of responses to thechange of parameter values [13]. It has been recog-nized as a powerful tool for systems biological ap-proaches due to its practical applicability to modelbuilding and evaluation, understanding system dy-namics, evaluating the confidence of a model under

– ( – ) – ( – )dd

chxt

g x xp x

x px x x5

1 5 41 4

2

42

22 2 5 4= +

+

xt

v g x x g C xq x

x q4

1 1 5 4 2 0 41 4

2

42

2( – ) ( – )–

dd

= ++ 22

2 5 41 4

2

42

22( – )–+

+

⎛

⎝⎜⎞

⎠⎟+v x x x

p xx p

Jr ch LTCC,,

uncertainties, and experimental design [14–16]. Ingeneral, sensitivity functions for parameter sensi-tivity analysis take the form

where M denotes the response of a system and Pdenotes a system parameter [17]. In this study, weemployed a relative sensitivity function known asthe LSF. LSF is dimensionless and thereby allowscomparison of physically different parameters [18].The LSF Tji is defined as follows:

(2)

where xj denotes the jth state variable, pi the ith parameter, and Δpi the change of the parameterpi.

3 Results

3.1 Dynamical analysis of the calcium signaling system

The T–O model adopted from Eq. (1) can be used toanalyze the Ca2+ dynamics under two different con-ditions: the graded Ca2+ dynamics according togradual stimuli and the self-oscillatory Ca2+ dy-namics according to the increased Ca2+ leakage

T tx t p

pp

x t px t

jij i

i

i

j i

j( )ln ( ; )

ln ( ; )(

=∂

∂= ×

∂ ;; )

( ; )( ; )– ( ; )

pp

px t p

x t p p x t p

i

i

i

j i

j i i j i

∂≈

×+ Δ

Δppi

SMM

PP

MPM =

∂

∂ =Percentage change inPercentage chaange in P

Table 1. Nominal parameter values used for simulations [12]

Compartment Parameter Value (unit) Description

RyR a1 15 (s−1⋅μM−1) Association rate of Ca2+ to the positive regulatory sited1 7.6 (s−1) Dissociation rate of Ca2+ from the positive regulatory sitea2 0.8 (s−1⋅μM−1) Association rate of Ca2+ to the negative regulatory sited2 0.84 (s−1) Dissociation rate of Ca2+ from the negative regulatory sitech 80.0 (s−1) Channel conductance

SERCA p1 1.038 × 103 (μM⋅s−1) Maximum pumping ratep2 0.12 (μM) Threshold coefficient

NCX q1 19.0 (μM⋅s−1) Maximum exchange rateq2 0.06 (μM) Threshold coefficient

Extracellular medium C0 1.5 × 103 (μM) Ca2+ concentrationCytoplasm vr 0.185 Volume ratio

g1 0.4 (s−1) Leakage coefficient from SR to the cytoplasmg2 1.093 × 10−2 (s−1)a) Leakage coefficient from the extracellular medium to the cytoplasm

a) This value of the leakage coefficient g2 is used to generate sustained oscillations for cytosolic Ca2+ concentration under no stimulated Ca2+ influx through the LTCC.In this case, the initial condition x(0) = (0.5343, 0.1130, 0.0616, 0.0955, 41.1403) is used for simulation that was obtained from the sustained oscillatory dynamics of the intracellular Ca2+ and the open fraction of RyR. For a slowly damped cytosolic Ca2+ concentration under induced Ca2+ influx through LTCC, g2 = 1.063 × 10–2 isused [12] and a steady-state value x(0) = (0.6962, 0.1883, 0.0246, 0.1370, 38.1262) is used for simulation.

Figure 3. The state transition diagram of RyR [12]. The positive (negative)regulatory Ca2+ binding site is represented by + (–) inside a circle (asquare, respectively). Shaded circle and square represent Ca2+-boundsites.



from the extracellular medium into the cytoplasmthat can be caused by the physical damage of thesarcolemmal membrane [12]. First, we have inves-tigated the graded cytosolic Ca2+ dynamics of thecalcium signaling system given gradual stimulithrough LTCC (Fig. 4A). The input stimulus of Ca2+

influx (JLTCC) was given between 2 and 2.25 s.WhenJLTCC was less than the threshold value (3.75(μM/s)), the system showed a weak graded re-sponse and, as JLTCC has become larger than thethreshold value, the system showed a much moregraded response. When the system was over-stim-ulated (JLTCC>8.36), the system exhibited dampedoscillations with more than one significant pulse,and the frequency as well as the amplitude have in-creased according to the increasing Ca2+ influx.Then, we have explored the self-oscillatory cytoso-

lic Ca2+ dynamics with respect to the variation ofselected parameters: the Ca2+ leakage rate of thesarcolemmal membrane (g2: Fig. 4B), the maximumrate of NCX (q1: Fig. 4C), and the RyR channel con-ductance (ch: Fig. 4D). The system response alongwith the variation of g2 revealed four different Ca2+

dynamics: weak responses for g2<0.0107; a dam-ped-oscillatory behavior for 0.0107 ≤ g2<0.0109; asustained-oscillatory behavior with an increase inamplitude according to the increase in parametervalue over 0.0109 ≤ g2<0.0127; diverging responsesfor g2 ≥ 0.0127.The system response along with thevariation of q1 was symmetric with respect to thatof g2: diverging responses for q1<16.5; a sustained-oscillatory behavior with a decreasing amplitudeaccording to the increase in parameter value over16.5 ≤ q1<19.1; a damped-oscillatory behavior for

Figure 4. The intracellular Ca2+ dynamics under various cellular conditions. (A) The system response according to graded stimuli. Ca2+ influx with a con-stant amplitude (A0) is applied over 2–2.25 s. To generate a damped response in the resting myocyte g2 = 1.063 × 10−2 is used. The system response withrespect to the variation of the coefficient for the sarcolemmal membrane leakage from the extracellular medium to the cytoplasm (B), the maximum rate ofNCX (C), and the channel conductance of RyR (D).



19.1 ≤ q1<19.4; weak responses for q1 ≥ 19.4. Thesystem response along with the variation of ch ex-hibited three different Ca2+ dynamics: weak re-sponses for ch<54.8; a sustained-oscillatory behav-ior with a decrease in amplitude according to theincreasing parameter value over 54.8 ≤ ch<89.4; adamped-oscillatory behavior for ch ≥ 89.4.

The dynamical analysis of the calcium signalingsystem revealed that the sustained-oscillatory be-havior of the system is not induced by the externalstimulus (i.e., the Ca2+ influx through LTCC) butprimarily by the balance among system parame-ters. Furthermore, we found that the dynamicalanalysis for g2 = 1.093 × 10−2 exhibited a sustained-oscillatory behavior over a large range of parame-ter variations (Figs. 4B–D). Hence, the Ca2+ leakagerate of the sarcolemmal membrane from the extra-cellular medium into the cytoplasm (g2) seems toplay a dominant role in determining the self-oscil-latory behavior of the Ca2+ dynamics.

3.2 LSA

To further analyze the influence of system param-eters on the Ca2+ dynamics in the calcium signalingsystem showing a self-oscillatory behavior, we havecarried out the LSA on the open fraction of RyR andthe Ca2+ concentration in the cytoplasm and SRwith respect to the following five parameters: themaximum rates of SERCA (p1) and NCX (q1), theleakage rates of the SR membrane (g1) and sar-colemmal membrane (g2), and the RyR channelconductance (ch). Therefore, there are 25 LSFs tobe calculated since both i and j are five in this case.An LSF Tji is obtained by solving Eq. (2) numeri-cally using MATLAB subject to 0.1% parameterchanges (i.e., Δpi = 0.001 × pi). LSA has been done

only for one cycle of the self-oscillatory Ca2+ dy-namics since the system shows sustained oscilla-tions (the dashed line in Fig. 5).

The simulation result of LSA revealed that theoverall Ca2+ dynamics is mainly influenced by theleakage rate of the sarcolemmal membrane (g2),the maximum pump rate of NCX (q1), the channelconductance of RyR (ch), and the maximum pumprate of SERCA (p1) whereas the leakage rate of theSR membrane (g1) has little effect compared tothese parameters (Figs. 6B and C). The upstrokephase of the cytosolic Ca2+, in which the cytosolicCa2+ concentration is abruptly elevated, was posi-tively regulated by g2 and ch while q1 and p1 hadnegative regulatory effects (Fig. 6B). More specifi-cally, the cytosolic Ca2+ concentration showed themost positive (negative) sensitivity to g2 (q1, re-spectively).The sensitivity then dropped as the cy-tosolic Ca2+ level approached its peak. In the relax-ation phase, in which the cytosolic Ca2+ concentra-tion decreases gradually, the roles of g2, q1, ch, andp1 were reversed: g2 and ch played negative regula-tory roles while q1 and p1 played positive regulato-ry roles. The sensitivity of the cytosolic Ca2+ in-creased to its second peak as its concentration ap-proached the resting level (the end of the relax-ation phase). After the relaxation phase, thesensitivity approached zero and the cytosolic Ca2+

concentration was maintained at the resting leveluntil another cycle began.The sensitivity curves ofthe SR Ca2+ concentration for the selected param-eters exhibited reverse images to those of the cy-tosolic Ca2+ concentration (Fig. 6C). Note that itsphase lagged behind that of the cytosolic Ca2+. Thesensitivity curves of the open fraction of RyRshowed similar characteristics to those of the cy-tosolic Ca2+ (Fig. 6A).

Figure 5. Dynamics of the fraction ratio of RyR (the upper panel) and the normalized Ca2+ concentrations inSR and the cytoplasm (the lower panel).



4 Discussion

In this paper, the Ca2+ dynamics of cardiac my-ocytes have been investigated based on an experi-mentally well validated model. The dynamicalanalysis of the calcium signaling system revealedthat the behavior of Ca2+ dynamics depends on thebalance among the system parameters. We foundthat the system response with respect to the leak-age rate of the sarcolemmal membrane (g2) is sym-metric to that of the maximum rate of NCX (q1).

This is because the Ca2+ leakage of the sarcolem-mal membrane takes extracellular Ca2+ into the cy-toplasm while NCX pumps out the cytosolic Ca2+ tothe extracellular medium. If the leakage rate of thesarcolemmal membrane exceeded the NCX capac-ity, Ca2+ was accumulated in the cytoplasm andthereby exhibited diverging responses. In contrast,the system showed a weak response when the NCXcapacity exceeded the leakage rate of the sar-colemmal membrane. For the range of parameterswhose leakage rates through the sarcolemmal

Figure 6. The LSA of the open fraction of RyR (A), the cy-tosolic Ca2+ (B), and the SR Ca2+ (C) with respect to theselected parameters: the maximum rate of SERCA (p1),the maximum rate of NCX (q1), the leakage coefficientfrom SR to the cytoplasm (g1), the leakage coefficientfrom the extracellular medium to the cytoplasm (g2), and the channel conductance of RyR (ch). 0.1% parameterperturbation has been applied for the LSA (i.e.,Δpi = 0.001 × pi).



membrane and the NCX capacity were balanced,the system showed a sustained-oscillatory behav-ior.

In the LSA, the self-oscillatory Ca2+ dynamicsexhibited highest sensitivity to the leakage rate ofthe sarcolemmal membrane (g2) and the maximumrate of NCX (q1) in the upstroke and the relaxationphase of the cytosolic Ca2+.The temporal sensitivi-ties to these two parameters were symmetric withrespect to the time-axis since g2 and q1 correspondto the Ca2+ influx and efflux through the sarcolem-mal membrane, respectively. Similar interpretationalso applies to the symmetric profiles of the maxi-mum rate of SERCA (p1) and the RyR channel con-ductance (ch) where these correspond to the Ca2+

influx and efflux of SR, respectively.The fact we found through LSA that the intra-

cellular Ca2+ dynamics are more sensitive to NCXthan SERCA can be supported by the following ex-perimental results: Shannon and Bers [5] analyzedthe functional regulatory effects of SERCA andNCX on the SR Ca2+ content based on a mathemat-ical model of the rabbit cardiac myocytes. NCX wasshown to have a more significant effect than SER-CA in this experiment where the functional activi-ty of NCX was increased and that of SERCA was de-creased from the nominal value. On the other hand,another sensitivity analysis using a different math-ematical model of the rat ventricular myocytes re-vealed that SERCA is more sensitive than NCX(nonpublished data). This inconsistency might becaused by the different cellular contexts consid-ered in different mathematical models. For in-stance, the self-oscillatory Ca2+ dynamics of theT–O model is attributed by the membrane damageand subsequent increase of the Ca2+ leakage rateacross the sarcolemmal membrane while the Ca2+

oscillations of the rat ventricular myocytes is in-duced by periodic stimulus currents.

Circulation of the cytosolic Ca2+ in the cardiacmyocytes is primarily regulated by the two loops(Fig. 2): the external loop and the internal loop.Theexternal loop mediated by the Ca2+ leakage of thesarcolemmal membrane (and/or LTCC) and NCXcirculates the cytosolic Ca2+ around the extracellu-lar medium and the cytoplasm. The internal loopmediated by SERCA and RyR circulates the cytoso-lic Ca2+ around SR and the cytoplasm. It was re-ported that the internal loop mediated by SERCA isresponsible for 70% (92%) of the whole cytosolicCa2+ circulation, the external loop by NCX for 28%(7%), and other slow processes for only about 1%(1%) in the ventricles of rabbit and guinea pig (inthe ventricles of rat and mouse, respectively) [1]. Incontrast, the result of our LSA suggests that the ex-ternal loop has a more significant effect in regulat-

ing the cytosolic Ca2+ than the internal loop in theself-oscillatory cardiac myocytes.This might be be-cause the increased Ca2+ leakage due to the physi-cal damage of the sarcolemmal membrane has amore significant effect on the intracellular Ca2+ dy-namics than other components.

In general, the results of sensitivity analysishinge upon the validity of the underlying model. Inother words, the results of the LSA might varyamong the different models. Moreover, differentinitial conditions might also result in different be-haviors of the Ca2+ dynamics. However, the LSA isstill a powerful tool for selecting the most signifi-cant target parameters in the regulation of systemdynamics. Throughout this process, some new in-sights into the disease mechanisms associated withthe alteration of system parameters can be ob-tained.

This work was supported by the Korea Science andEngineering Foundation (KOSEF) grant funded bythe Korea government (MOST) (M10503010001-07N030100112) and also supported from the KoreaMinistry of Science and Technology through the Nu-clear Research Grant (M20708000001-07B0800-00110) and the 21C Frontier Microbial Genomics andApplication Center Program (Grant MG05-0204-3-0).

The authors have declared no conflict of interest.

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