Sensing Cell-Culture Assays with Low-Cost Circuitry

1 SciEn iFic RePOR S | (2018) 8:8841 | DOI:10.1038/s41598-018-27295-3 www.na u e.com/scien i ic epo s Sensing Cell-Cul u e Assays wi h Low-Cos Ci cui y Pablo Pé ez2,4, Glo ia Hue as2,3, And és Maldonado-Jacobi2, Ma ía Ma ín1, Juan A. Se ano2, Albe o Olmo2,4, Paula Daza1 & Albe o Yú e a 2,4 An al e na i e app oach o cell-cul u e end-poin p o ocols is p oposed he ein. This new echnique is sui able o eal- ime emo e sensing. I is based on Elec ical Cell-subs a e Impedance Spec oscopy (ECIS) and employs he Oscilla ion-Based Tes (OBT) me hod. Simple and s aigh o wa d ci cui blocks o m he basis o he p oposed measu emen sys em. Oscilla ion pa ame e s – equency and ampli ude – cons i u e he ou come, di ec ly co ela ed wi h he cul u e s a us. A use can emo ely ack he e olu ion o cell cul u es in eal ime o e he comple e expe imen h ough a web ool con inuously displaying he acqui ed da a. Expe imen s ca ied ou wi h comme cial elec odes and a well- es ablished cell line (AA8) a e desc ibed, ob aining he cell numbe in eal ime om g ow h assays. The elec odes ha e been elec ically cha ac e ized along he design low in o de o p edic he sys em pe o mance and he sensi i i y cu es. Cu es o 1-week cell g ow h a e epo ed. The ob ained expe imen al esul s alida e he p oposed OBT o cell-cul u e cha ac e iza ion. Fu he mo e, he p oposed elec ode model p o ides a good app oxima ion o he cell numbe and he ime e olu ion o he s udied cul u es. End-poin cell-cul u e p o ocols ha e been, and a e being, ex ensi ely employed in many assays o cha ac e i- za ion o cell p ope ies a biology labs. These assays allow obse ing nume ous biological p ocesses. Thei inal goal is ypically o analyse he cell popula ion in a dish o Pe i pla e as a measu ed esponse o consequence om a gi en ex e nal s imulus o biomedical ea men . These classical p o ocols equi e a la ge quan i y o samples. They a e expensi e in e ms o bo h ma e ial and human e o 1. Al e na i ely, Elec ical Cell-subs a e Impedance Spec oscopy (ECIS)2,3 ep esen s a ma u e me hod enabling eal- ime acquisi ion o biological pa ame e s (numbe o cells, cell ac i i y, mo ili y and size) h ough he measu emen o he cell-cul u e imped- ance4–6. I can be also applied o any kind o cell in ela ion wi h he en i onmen 3,7,8. ECIS has he ad an age o being non-in asi e. Unlike end-poin p o ocols, i a oids he dea h o cells o e ime. ECIS is also ela i ely inexpensi e since only one sample o Pe i pla e is equi ed o a pe o mance cu e. Two main aspec s mus be conside ed when i comes o implemen ing ECIS. Fi s , in o de o p ope ly pe - o m accu a e bio-impedance measu emen s, adequa e ci cui s mus be selec ed acco ding o he a ge ed meas- u emen echnique9,10. The accu acy o he ob ained esul s will join ly depend on he e iciency and p ecision o his echnique along wi h he ine pe o mance o i s ci cui ealiza ion. Secondly, i is necessa y o de elop eliable elec ical models o elec odes and cells. These models a e mean o ansla e measu emen s in o answe s o he undamen al ques ion: how many cells a e in he cul u e7,11,12? Se e al cell-elec ode elec ical models ha e been epo ed in he li e a u e. Fo ins ance, magni ude and phase impedance ha e been de i ed using a i s -o de RC model2. In u n, his model gi es ise o ano he one based on h ee pa ame e s: Rb, he ba ie esis ance be ween cells; h, he cell-elec ode dis ance; and cell, he cell adius. As an al e na i e, Fini e Elemen Simula ions (FEM)11,12 can be execu ed o sol ing he elec ical ield ac oss he whole s uc u e. This me hod in oduces a new pa ame e o he model, Rgap, desc ibing he gap o cell-elec ode in e ace esis ance. These wo models ex ac ed om he li e a u e conside ei he he cell con luen phase2 o a ixed a ea co e ed by cells11,12. Bo h a o emen ioned poin s, i.e. sui able ci cui y and p ope modelling, a e open esea ch p oblems o biomed- ical enginee ing hese days. 1D o. Biología Celula , Facul ad de Biología, Uni e sidad de Se illa, A . Reina Me cedes no 6, 41012, Se illa, Spain. 2Ins i u o de Mic oelec ónica de Se illa, IMSE, Uni e sidad de Se illa, A . Amé ico Vespucio sn, 41092, Se illa, Spain. 3D o. de Elec ónica y Elec omagne ismo, Facul ad de Física, Uni e sidad de Se illa, A . Reina Me cedes sn, 41012, Se illa, Spain. 4D o. Tecnología Elec ónica, Escuela Técnica Supe io de Ingenie ía In o má ica, Uni e sidad de Se illa, A . Reina Me cedes sn, 41012, Se illa, Spain. Co espondence and eques s o ma e ials should be add essed o P.D. (email: [email p o ec ed]) o A.Y. (email: [email p o ec ed]) Recei ed: 5 Janua y 2018 Accep ed: 30 May 2018 Published: xx xx xxxx OPEN www.na u e.com/scien i ic epo s/ 2 SciEn iFic RePOR S | (2018) 8:8841 | DOI:10.1038/s41598-018-27295-3 In his wo k, a sys em o eal- ime moni o ing o cell cul u e assays om any in e ne -connec ed de ice (lap op, cellula phone, e c) is p oposed. The unde lying ci cui s a e simple because hey di ec ly a ise om he p oposed bio-impedance echnique. The e a e no s ong speci ica ions ei he o he Common-Mode Rejec ion Ra io (CMRR) in ins umen a ion ampli ie s13 usually equi ed o da a acquisi ion, o o accu a e AC ol age/ cu en signal gene a o s wi h p og ammable equency o signal exci a ion14,15. The p oposed ci cui y meas- u es he cell cul u e s a e by inse ing i in a closed-loop oscilla o . As a esul , he equency and ampli ude o he quasi-sinusoidal ou pu oscilla ions a e a unc ion o he cell numbe in he cul u e. The expec ed sensi i i y cu es o he sys em a e heo e ically ob ained om he cell size and densi y, and he p oposed elec ode model. The manusc ip is s uc u ed as ollows. Ma e ial and me hods sec ion desc ibes he applied assay p o ocol. This sec ion also includes he elec ode-solu ion model (in ou case, cul u e medium) use ul o cell-elec ode cha ac e iza ion as well as he p ocedu e o de elop meaning ul cell-mic oelec ode models. The implemen ed ci cui blocks a e hen desc ibed and hei main unc ionali ies, along wi h he design o he sensi i i y cu es de i ed o elec ical measu emen . Expe imen s ca ied ou o model comme cial elec odes, and hei applica ion o eal- ime cell cul u e moni o ing assays, a e p esen ed in Expe imen al esul s sec ion. Finally, Conclusions sec ion summa izes ou esul s, compa ing hem wi h he esul s ob ained om he classical Pe i pla e based me hod o cell cul u e es . Ma e ial and Me hods Cell line and cul u e condi ions. The cell cul u e was ca ied ou on a Chinese hams e o a y ib oblas cell line, AA8 (Ame ican Type Cul u e Collec ion). AA8 cells we e cul u ed in McCoy’s medium supplemen ed wi h 10% ( / ) oe al cal se um, 2 mM L-glu amine, 50 μg/ml s ep omycin, and 50 U/ml penicillin. Cells we e ou inely sub-cul u ed. The cell line was main ained a 37 °C in a humidi ied a mosphe e wi h 5% CO2. They we e always in exponen ial g ow h phase du ing he expe imen s. Elec odes. Comme cial elec odes 8W10E PET, om Applied Biophysics (AB)16, we e employed o cell cul- u e assays (h p://www.biophysics.com/). This mul i-well is composed o eigh sepa a ed wells, each one includ- ing en ci cula 250- μm diame e bio-compa ible gold mic oelec odes. Cell g ow h. We conduc ed a basic g ow h assay. Cells we e a in he incuba o du ing one week. They we e ini ially pla ed a a densi y o 2500, 5000 and 10000 cells/0.8 cm2 in mul i-wells om AB. Cell g ow h was meas- u ed o se en days, wi h an obse a ion pe iod o 1 hou o each well ime e olu ion om he beginning o he expe imen . Pe i-pla e cul u es we e also conduc ed, ea u ing he same cell densi y o he sake o u he com- pa ison wi h he p oposed bio-impedance es . Elec ode-elec oly e model. The elec ode impedance in ionic liquids has been widely s udied in he li e a u e7,11. The main componen s iden i ying he elec ical pe o mance o a me al elec ode inside a solu ion a e ou , as illus a ed in Fig.1A: (1) CI, he double laye capaci ance; (2) Rc , he ans e esis ance, modelling he cu en lowing h ough he elec i ied in e ace; (3) ZW, he Wa bu g impedance, due o limi ed mass di usion om elec ode su ace o solu ion. The elec on ans e esis ance Rc is in se ies wi h he limi ed mass di usion impedance ZW, which is only ele an a e y low equencies. Finally, (4) Rs, he sp eading esis ance, ha con- side he cu en a elling ac oss he bulk solu ion. These ou elemen s depend on he echnology, medium and geome y. A small AC ol age signal mus be applied as an exci a ion o wo k in linea egion7. Figu e 1. (A) Elec ical model componen s o one elec ode in con ac wi h an ionic solu ion. (B) Simpli ied and a ea-no malized model in Fig.1A wi hou Wa bu g impedance. Z(ω) ep esen s CI||Rc . (C) P oposed model o cell-elec ode using a Rgap esis ance – which models he cu en lowing in pa allel h ough he in e ace be ween he elec ode and cell, depending on he elec ode-cell dis ance – and he ill ac o pa ame e ( = Ac/A). A is he elec ode sensing a ea whe eas Ac is he elec ode sensing a ea co e ed by he a ached cells. (D) Illus a ion o he Rgap e ec . The cu en lows om elec ode e1 o e2, as a esponse o an applied AC ol age. www.na u e.com/scien i ic epo s/ 3 SciEn iFic RePOR S | (2018) 8:8841 | DOI:10.1038/s41598-018-27295-3 Cell-elec ode model. Ou p ac ical se up o 8W10E PET cul u ewa es is depic ed in Fig.2. A wo-elec ode impedance senso is used: e1 is he sensing elec ode comp ising 10 pa allel 250- μm diame e gold elec odes; e2 is he e e ence, usually g ound-connec ed2. Since he a ea o e2 is much la ge han ha o e1, he cell loca ion, numbe and size a e1 cons i u e he a ge o be de ec ed (Fig.2C). The model in Fig.1C implici ly assumes ha he sensing a ea o e1 could be o ally o pa ially illed by cells. Fo he wo-elec ode senso shown in Fig.2B, a 10e1 sensing a ea is de ined by A, being Z(ω) he impedance pe uni a ea o he emp y elec ode. i.e. wi h no cells on op. Conside ing pa ial co e age o he elec odes, le Ac deno e he cell-co e ed su ace on elec ode e1. The impedance esponse associa ed o a non-co e ed o emp y su ace is de ined by Z(ω)/(A − Ac) whe eas Z(ω)/Ac is he impedance o he co e ed a ea. The esis ance Rgap con- side s he cu en lowing la e ally h ough he elec ode-cell in e ace. Fo an emp y elec ode, he impedance model Z(ω) co esponds o he ci cui in Fig.1B. The e2 elec ode is no mally la ge and connec ed o g ound. I s impedance is small enough o be neglec ed. The pa ame e , called ill ac o , equals ze o o Ac = 0 – ha is, o no cell co e age on e1 elec odes – and one o Ac = A – ha is, o ull cell co e age on e1 elec odes. Finally, Zc ( = 0) = Z(ω) is he magni ude o he elec ode impedance wi h no cells. The ill ac o is hus employed, oge he wi h he es ima ed cell size, o de e mine he a ea co e ed by he cells and he cell numbe . Implemen ed ci cui . The p oposed ci cui o bio-impedance measu emen s a oids he use o high-pe o mance9,17,18 ci cui y o equipmen , as well as he need o accu a e cu en / ol age gene a- o s15, ins umen a ion ampli ie s13 and p ecise demodula ion ci cui s10. This is accomplished by u ning he bio-impedance in o a ol age oscilla o whose oscilla ion pa ame e s ( osc, aosc) a e dependen on and p opo ional o he biological sample unde es . A simpli ied ci cui diag am is depic ed in Fig.3. Cell cul u es a e inco po- a ed o ci cui analysis h ough he elec ode-cell impedance, Zcell-elec ode, in oduced when cells a e being cul- u ed on ECIS elec odes. The Zcell-elec ode is included a he Hz(s) block in Fig.3. Ci cui design is he e o e d i en no o a maximum no malized esis ance alue8, bu o op imal ci cui oscilla ion condi ions19. This ci cui y wo ks as a ol age oscilla o . I is cha ac e ized by wo oscilla ion pa ame e s: osc and aosc a he ou pu ol age sig- nal Vcell. The ci cui ob ains oscilla ion pa ame e s co ela ed wi h he cell numbe , acco ding o he elec ode-cell model p e iously desc ibed, o simila ly wi h he ill ac o pa ame e . This p ocess is moni o ed in eal ime using a emo e sensing sys em20. The simpli ied block diag am is shown in Fig.3 whe eas he ci cui schema ics a e depic ed in Fig.4. The building blocks o hese ci cui s a e ope a ional ampli ie s, esis ances and capaci o s. The second-o de Band-Pass Fil e (BPF) allows he selec ion o he equency a which he oscilla o is uned. The Q ac o mus be high enough o educe he o al ha monic dis o ion a he ol age oscilla ion signal (Vcell) bu also low enough o pe mi a wide equency dynamic ange. In his pa icula case, Q = 10. The BPF cu -o equency, o = 1 kHz, was se acco ding o he ea u es o bo h he eedback loop and he bio-impedance sam- ple o be sensed. The ampli ude o he ol age Vcell suppo ed by he cul u e is limi ed o p ese e he linea esponse o he elec odes. Likewise, he cu en h ough he cell cul u e is limi ed o a maximum ampli ude le el o 20 µA. The BPF ci cui s a e shown in Fig.4A. The bio-impedance block is depic ed in Fig.4B. I is buil upon Figu e 2. (A) 8W10E PET cul u ewa e om AB16 wi h 8 wells o 0.8 cm2. (B) Cells a e measu ed on op o he 10 ci cula gold elec odes, e1 (Aelec), wi h o al elec ode a ea A = 10 × Aelec. The sensing a ea is he sum o he 10 e1 gold elec odes, (A). (C) Pho omic og aph o AA8 cells pa ially co e ing he a ea Aelec o a ci cula elec ode. Figu e 3. Simpli ied ci cui block diag am p oposed o measu emen . I comp ises he bio-impedance block Hz(s), including Zcell-elec ode, he compa a o – K, HCMP,F(s) and CMP – and he band-pass il e HBP(s). www.na u e.com/scien i ic epo s/ 4 SciEn iFic RePOR S | (2018) 8:8841 | DOI:10.1038/s41598-018-27295-3 a cu en sou ce, IZc, which is independen o he cell load hanks o a eedback pa h. I s unc ion is o inse he elec ode-cell impedance a he closed-loop ans e unc ion. The ou pu ol age, Vcell, is limi ed o 50 mV in o de o a ain linea esponse om he elec odes. To mul iplex he eigh elec ode channels, a modi ied ampli ie is employed o ensu e ha all o he elec odes – excep o hose ones being measu ed – ha e bo h e minals e1 and e2 connec ed o g ound. The compa a o ci cui is shown in Fig.4C. I inco po a es a hys e esis window o inpu noise educ ion ha inc eases he loop s abili y in he oscilla o esponse. P io o he compa a o , he low and high equency componen s o he ol age signal Vcell a e emo ed by a band pass il e – HPF in se ies wi h a LPF in HCMP,F(s). This signal is also ampli ied by a ac o K = 100, simpli ying he compa a o ope a ion. The da a acquisi ion and wi eless communica ion unc ionali ies ely on a ious digi al de ices, including a digi al sec ion based on an ARM Co ex-M7 mic ocon olle de ice. This de ice has a ich se o pe iphe als. In pa icula , we exploi i s Analog o Digi al Con e e s (ADCs) o sampling da a, and i s Real-Time Clock (RTC) o synch oni- za ion. Gene al-pu pose inpu -ou pu pins om he mic ocon olle can ac i a e he analog signals and mul iplex he wells o he sampled. Fu he mo e, ARM Co ex-M7 de ices implemen a Floa ing Poin Uni (FPU) enabling hem o on-chip execu ion o signal p ocessing algo i hms. A Blue oo h module was included in he sys em o Figu e 4. Ci cui s schema ics employed o (A) Band-Pass Fil e (BPF), (B) Bio-impedance block and (C) Compa a o . www.na u e.com/scien i ic epo s/ 5 SciEn iFic RePOR S | (2018) 8:8841 | DOI:10.1038/s41598-018-27295-3 acili a e wi eless communica ion. The µP sys em inside he cell-cul u e incuba o chambe is in s andby mode mos o he ime. The sys em is ba e y powe ed wi h a model Ansmann 7.4 V Li, being he powe consump ion o a week assay o 985 mW. The a iables o expe imen con ol (sample ime, o ins ance), can be de ined and modi ied by he use ia he web applica ion. This in e ace also shows he da a collec ed om he expe imen in eal ime. The da a plo ed on he web applica ion a e he equency and he ampli ude ob ained om he mic o- elec odes, i.e. he Vcell signal. The in e ace ope a es in eal ime and online. I can be checked on h p://ja is.d e. us.es/mixcell. None o he physical, chemical o biological ac o s o he expe imen s a e a ec ed by he wi eless communica ion. Tempe a u e, humidi y and ba e y ol age le el a e con inuously measu ed by he sys em. Impedance measu emen s wi h he HP 8591A Spec um Analyse . A HP 8591A Spec um Analyse 21 was used o ob ain he magni ude and phase o Bode plo s o elec ode cha ac e iza ion, bo h wi h medium only and including also cells. This cha ac e iza ion was equi ed o selec he co ec ope a ion e- quency ange o he p oposed oscilla o du ing i s ini ial design s age. Expe imen al Resul s Elec ode Model. The HP 8591 A Spec um Analyse oge he wi h an in e ing ampli ie wi h 34.9-dB DC gain we e employed o ca y ou a pe o mance es aiming a measu ing he h ee componen s o he elec ical model o 8W10E PET, namely CI, Rc and Rs, in con ac wi h medium. This es also ende ed he impedance componen s o he elec odes in addi ion o he medium e sus equency cha ac e is ic – magni ude and phase. Pole-ze o ex ac ion om impedance Bode plo s cons i u es a i s app oach o ex ac elec ode pa ame e s. In Fig.5A, a pole is loca ed a a ound 8 Hz o wells 2 and 6 wi h medium, while a ze o is loca ed a 10 kHz, leading o Rc = 618 k Ω, CI = 32.2 nF and Rs = 495 Ω. These alues a e used o ini ial calcula ions when an elec ode-me- dium elec ical model is equi ed, o example, du ing he design o he ci cui in Fig.3. Howe e , wo e ec s mus be ca e ully conside ed in his p ocess: i s , he dispe sion alues om well o well; second, he ime e olu- ion o elec ode pa ame e s due o elec ochemical ac i i y on he elec ode- o-medium in e ace along assays. Cell-Elec ode Model. F om he elec ode-medium elec ical model jus de ined, we can de i e he co - esponding cell-elec ode elec ical model based on h ee undamen al pa ame e s: he ill ac o ( ), he elec- ode a ea (A), and he esis ance o he gap sec ion (Rgap) illus a ed in Fig.1C. A measu emen simila o he one desc ibed in he p e ious sec ion was ca ied ou in an expe imen whe e cells g ew on op o ECIS elec- odes. The magni ude and phase impedance esponses pe well we e measu ed o i e days wi h he HP 8591A Spec um Analyse . The esponses o day 1 and 5 a e depic ed in Fig.5. These measu emen s p o e ha signi i- can changes on magni ude and phase occu due o he inc easing numbe o cells. No ably, phase changes ma ch he a ge ed e olu ion o he selec ed band-pass il e peak equency in he OBT eedback, he eby achie ing good equency sensi i i ies. Following a simila p ocess as he p e ious sec ion, we ob ain he elec ode pa ame e s CI, Rc , Rs and Rgap, as well as ma ching alues o Rgap in he ange o (500 Ω, 1000 Ω). Howe e , we mus highligh ha (1) o he medium wells, he elec ode pe o mance changes o e ime and, (2) be ween equal wells, hei pe o mance also changes due o misma ching e ec s, so he elec ode pa ame e s will be di e en om well o well and will also a y o e ime. Bo h e ec s make i di icul o ind eliable pa ame e alues o he elec ical elec ode model. Figu e 5. Impedance spec um o one 8W10E PET elec ode, bo h wi h medium and cells: magni ude and phase esponses, measu ed wi h he HP-8591A a day 1 (A) and day 5 (B) o he expe imen , o W1: 2500 cells, W2 and W6: medium. W4: 5000 cells, W7 and W8: 10000 cells. www.na u e.com/scien i ic epo s/ 6 SciEn iFic RePOR S | (2018) 8:8841 | DOI:10.1038/s41598-018-27295-3 Ci cui expec ed pe o mance: equency and ampli ude anges. Acco ding o hese expe imen- al alues o he elec ode and cell elec ical pa ame e models, we an simula ions o e alua e he expec ed equency and ampli ude anges o he obse ed oscilla ion when cells we e g owing in a cul u e. These simula- ions also guided he design o he p oposed ci cui s. Fi s ly, elec ical simula ions p o ided he equency and ampli ude esponse o he p oposed OBT sys em when inc eases om 0 h ough 1 (cell g ow h). The ci cui model shown in Fig.1C was selec ed o emula e his scena io, se ing = 0 o elec odes wi h no cells, and = 1 a con luence o monolaye s a e. Ini ial elec ode pa ame e alues we e es ima ed om measu ed impedance esponses in Fig.5. They we e hen i ed conside ing he ini ial and inal alues (pla eau phase) o equency and ampli ude measu ed a Vcell in he 5000-cell case. In o de o ha e a model o he ansien e olu ion o he e- quency and ampli ude esponses in he sys em, we ha e es ima ed he ime e olu ion o ( ) om an exponen ial cell g ow h dependence: π =.. . kN A () 2 (1) o k cell well 2 whe e No is he ini ial numbe o cells seeded a he well, k is he ac ual numbe o cell cycles ( ime in hou s di ided by he cell di ision cycle, in his case 18 h), cell is he cell adius (a ound 10 μm) and Awell is he 8W10E PET well a ea (0.8 cm2). Equa ion (1) ende s an app oxima ed alue o he ill ac o , plo ed in Fig.6 o an ini ial alue o 5000 cells. Elec ical simula ions de i ed om his ime dependence p oduce Fig.7(A–D) o equency and ampli ude esponses acco ding o he elec ode pa ame e alues Rc , CI, Rs p e iously calcula ed, and Rgap = 600 Ω. Cell g ow h moni o ing. Cell g ow h assays we e pe o med wi h AA8 cell line o alida e he implemen ed measu emen ci cui s. We also sea ch i ing ou model wi h he ac ual mic oelec ode-cell sys em and ex ac el- e an biome ic da a, in his case, cell numbe o ill ac o s. ime. In ou se up, we ini ially seeded he medium wi h 2500 cells (W1, W3), 5000 cells (W4, W5) and 10000 cells (W7, W8) in o sepa a e well pai s. Two wells (W2 and W6) only con ained cul u e medium. The eigh wells we e sequen ially measu ed by in oducing each well as he Zcell-elec ode impedance in o he closed-loop eedback pa h in Fig.3. Figu e8A shows he equency e olu ion o e ime ha we measu ed o se en days using 8W10E PET senso s wi h ou ci cui p o o ype19. Fu he mo e, he ampli udes measu ed a he ou pu ol age, Vcell, a e plo ed in Fig.8B. The sample ime was one hou , being his pa ame e comple ely unable by he use . The equency e olu ion p o es ha he equency, e ec i ely, inc eases o e ime as a consequence o inc easing impedance caused by he g owing numbe o cells a ached o he elec odes, as i was expec ed om Fig.7C. Ini ially, he cells equi e some ime o adap and ecognize each well, so cell p oli e a ion ac ually s a s a e a ound 24 hou s, o e en la e . A he beginning o he expe imen , he e a e no cells on he sensing elec odes in p ac ical e ms. The same equency should he e o e be meas- u ed in all o he wells, e en a W2 and W6 whe e he e was only medium. Howe e , his ini ial alue (called ini) anges om 770 Hz (W5) h ough 850 Hz (W8). This means ha he elec ode pe o mance ob ained om i s elec ical model could p esen dispe sion alues due o elec ode misma ching. In addi ion, he F equency Dynamic Range (FDR = max − min) a ies o each well: he maximum is o W7 whe eas he minimum occu s o wells W1 and W5. This could also be caused by elec ode misma ching. The equency e olu ion o wells wi h medium (W2, W6) dec eases o e ime. This could be in e p e ed as a dynamic e olu ion o elec ical p ope ies in elec ode-medium in e ace owing o elec ochemical eac ions7. Acco ding o his esul , he elec ode model changes o e ime, so i is no qui e co ec o conside a “s a ic alue” o Rc , CI and Rs componen s du ing he assay pe iod. On he o he hand, he ampli ude e olu ion in Fig.8B p esen s a simila beha iou , as depic ed in Fig.7D. I inc eases om an ini ial alue, aini, di e en om well o well, up o he con luence o pla eau phase. Figu e 6. Expec ed alues a ained om Eq. (1) o es ima e he ill ac o s. ime o No = 5000 cells. www.na u e.com/scien i ic epo s/ 7 SciEn iFic RePOR S | (2018) 8:8841 | DOI:10.1038/s41598-018-27295-3 The Ampli ude Dynamic Range (ADR = amax − amin) also a ies among wells. No e ha he ampli ude alues a e e y low (se e al milli ol s). This is imposed o limi he maximum ol age and cu en ampli ude h ough elec- odes and cells, espec i ely. The ampli ude a wells only wi h medium (W2 and W6) p esen s a sligh inc ease o e ime. I seems o be less sensi i e han he beha iou obse ed o he equency. T ansien signals a W7 a e shown in Fig.9 o 1 = 35 hou s, and 2 = 98 hou s. These signals a e di ec ly sampled by he uC ARM, and p ocessed subsequen ly. To compa e equency and ampli ude e olu ion a di e en wells, we ha e no malized bo h esponses de ining he no malized equency and ampli ude as ollows: Figu e 7. F equency and ampli ude alues ob ained om elec ical simula ions o he sys em in Fig.3. The elec ode pa ame e s a e expe imen ally ex ac ed, whe eas he p edic ion comes om Eq. (1). The alues o he cell-elec ode pa ame e s a e: Rc = 618 k Ω, CI = 32.2 nF, Rs = 495 Ω, and Rgap = 600 Ω. No = 5000 cells. (A) F equency s. ill ac o . (B) Ampli ude s. ill ac o . (C) F equency s. ime. (D) Ampli ude s. ime. Figu e 8. Measu ed ime e olu ion o he oscilla ion equency (A) and ampli ude (B) o he ol age signal Vcell. The cu es co espond o 2500 cells (W1, W3), 5000 cells (W4, W5) and 10000 cells (W7, W8), seeded a = 0 in o sepa a e well pai s. Wells W2 and W6 con ain only medium. Dips in Fig.8 a e due o noise in luence. Signals (cu en s and ol ages) on elec odes and cells mus be small enough o a oid damage in cells and p ese e he linea model o he elec ode-solu ion. These ac s inc ease he sensi i i y o measu emen s o noise sou ces and, dec eases he Signal- o-Noise Ra io (SNR) in measu emen s. www.na u e.com/scien i ic epo s/ 8 SciEn iFic RePOR S | (2018) 8:8841 | DOI:10.1038/s41598-018-27295-3 = − − () (2) no min maxmin = − − a a a aa () (3) no min maxmin Figu e10A,B depic hese no malized esponses. Bo h equency and ampli ude e olu ions show ha well W7 and W8, seeded wi h 10000 cells, eached i s he con luence s a e, while wells W1 and W3 eached his s a e he la es since hey we e seeded wi h 2500 cells. The ime delay o sea ch he pla eau phase o wells seeded wi h 2500, 5000 and 10000 cells, is a ound 18–20 hou s, i.e. a ound one di ision pe iod o he cell line being es ed. This demons a es ha ou esul s a e cohe en wi h he expec ed pe o mance. Conside ing a well a ea o 0.8 cm2, he equency sensi i i y a con luence phase is 100 Hz/0.8 × 108 μm2 = 1.25 × 10−6 Hz/μm2. I means ha o a ci cula cell o adius 10 μm, he sensi i i y is app oxima ely 4 × 10−4 Hz/cell = 0.4 mHz/cell. The sensi i i y is calcula ed di iding he dynamic ange o he equency in Table1 by he numbe o cells ha can be i in such well. A simila es ima ion o Vcell ampli udes ende s a sensi i i y o 0.03 μV/cell. Figu e 9. Time e olu ion o oscilla ion pa ame e s a W7 ex ac ed om he designed web page. F equency (A) and ampli ude (B) o he Vcell signal. T ansien signals a 1 = 35 hou s, osc = 824 Hz (C) and 2 = 98 hou s, osc = 923 Hz (D). No e ha a scaled ac o o 31 is applied o he ampli ude. Figu e 10. No malized equency (A) and ampli ude (B) measu ed a Vcell. The cu es co espond o 2500 cells (W1, W3), 5000 cells (W4, W5) and 10000 cells (W7, W8), seeded a = 0. www.na u e.com/scien i ic epo s/ 9 SciEn iFic RePOR S | (2018) 8:8841 | DOI:10.1038/s41598-018-27295-3 Discussion Se e al aspec s can be highligh ed om hese expe imen al esul s. Fi s , he bio-impedance o he cell cul u e can be indi ec ly moni o ed in eal ime by measu ing he equency and ampli ude om he p oposed ci cui s. These signals a e p opo ional o he cell cul u e bio-impedance, and hence o he numbe o cells. Second, he measu emen s pe o med o elec ode-medium cha ac e iza ion shows a la ge dispe sion om well o well when applying he elec ode pa ame e s p oposed in ou model. Mo eo e , he e is a ime dependence o equency and ampli ude esponses in he elec ode medium. This makes i impossible o ini ially i he elec ical model pa ame e s o he elec ode-solu ion and elec ode-solu ion-cell. We ha e ca ied ou a s udy o cell g ow h e olu ion based on cu es ob ained om he ci cui esponse. Fo his pu pose, we applied he senso models p e iously o mula ed. The equency and ampli ude o he oscilla ion we e measu ed. The esul s show ha cell g ow h can be cha ac e ized om hese measu emen s. They inc ease mono onically as a di ec consequence o he inc easing numbe o cells up o he pla eau phase. Thei inc emen a e is p opo ional o he ini ial numbe o cells seeded in he cul u e. An expe imen al alue o 0.4 mHz/cell has been es ima ed as sensi i i y o he equency esponse, and 0.03 μV/cell o he ampli ude esponse. The expec ed dynamic ange o equency and ampli ude de i ed om ou elec ical models does no exac ly ma ch he expe imen al esul s, as shown in Fig.8. These de ia ions could s em om dispe sion o he elec ode pa ame e s (CI, Rc , Rs, and Rgap). No e ha he es ing ci cui is always he same, in con as wi h he obse ed a ia ion o he pa ame e s in he elec ode-solu ion elec ical model o e ime. In his ega d, an al e na i e i ing p ocess o he Rs elec ode pa ame e was applied o e each indi idual well in o de o accu a ely p edic equency and ampli ude. In his p ocess, we conside ed he ini ial and inal measu emen s o equency and ampli ude, he cell size (10- μm adius) and an es ima ed cell di ision cycle o 18 hou s, leading o, =+Δ.RR R () (4) ssis n whe e Rsi is he ini ial alue o Rs calcula ed om he expe imen al ampli ude a = 0( = 0), and ΔRs is i s o al inc emen , calcula ed a he end o he expe imen o = 1. We se n = 4 o his app oach. These hypo he- ses, oge he wi h he ill ac o p edic ion gi en in Eq. (1) and he pole-ze o based i ing p ocess p e iously desc ibed, a e in eg a ed in he elec ical simula ions o he p oposed ci cui s. The esul s a e depic ed in Fig.11 in e ms o equency and ampli ude es ima ions o he h ee ini ial numbe s o seeded cells. The expe imen al measu emen s ma ch well he p edic ion o he h ee cases, alida ing he es ima ion o he ill ac o expec ed du ing he cell g owing p ocess. Well W1 W3 W4 W5 W7 W8 FDR [Hz] 94 114 101 93 123 93 ADR [mV] 4.60 7.65 7.00 4.85 9.19 7.60 Table 1. Dynamic ange expe imen ally obse ed o equency and ampli ude oscilla o y esponses. Figu e 11. Simula ed equency and ampli ude, wi h Rs in Eq. (4), measu ed in wells: (A) W1, 2500 cells, (B) W5 wi h 5000 cells and (C) W7 wi h 10000 cells. Elec ical simula ions include he models o cell-elec ode and he ci cui s employed o measu ing he cell cul u es.