Proc. Nail. Acad. Sci. U SA Vol. 8 8 , p p . 78%-7900, September 1991 Cell Biology Micromotion of mammalian cells measured electrically (cell motility/fibroblast behavior/nanometer motions/electrical measurements) IVAR GIAEVER A N D CHARLES R. KEESE School o f Science, Rensselaer Polytechnic Institute, Troy, NY 12180-3590 Contributed b y Ivar Giaever, M a y 1 6, 1991 ABSTRACT Motility is a fundamental property o f mam- malian cells that normally i s intissue culture b y time lapse microscopy where resolution i s limited b y t h e wavelength o f light. This paper examines a powerful electrical technique b y which cell motion i s quantitatively measured a t th e nanometer level. I n this method, t h e cells a r e cultured o n small evaporated gold electrodes carrying weak ac currents. A large change i n th e measured electrical impedance o f t h e electrodes i s observed when cells attach a n d spread o n these electrodes. When t h e impedance i s tracked a s a function o f time, fluctuations a r e observed that a r e a direct measure o f cell motion. Surprisingly, these fluctuations continue even when t h e cell layer becomes confluent. B y comparing t h e measured impedance with a theoretical model, i t i s clear that under these circumstances th e average motions o f t h e cell layer o f 1 n m c a n b e inferred from t h e measurements. W e refer t o this aspect of cell motility a s micromotion. electrode impedance. The impedance fluctuations, however, continue a s cell layers become confluent. To understand these results a n d t h e possible sources o f t h e fluctuations, w e have considered th e interaction o f cultured cells with th e electrode surface i n detail. It i s well known from interference reflection microscopy studiesthat cells i n culture attach t o t h e substratum b y small foot-like projections leaving spaces o r channels between the ventral side o f the cell a n d t h e substratum (8). T h e amount o f current flowing i n these channels, a n d hence t h e impedance o f t h e cell-covered electrode, will depend on th e applied ac frequency. W e have modeled this system a n d compared th e calculated impedance values a function o f frequency with those measured f o r confluent layers o f WI-38 a n d WI-38 VA13 cells. I n addition, we have calculated t o what degree changes i n various cell parameters will affect impedance measurements. Locomotion o f cells i n tissue culture h a s been widely ob- served, a s many metazoan cells have t h e ability to crawl upon surfaces. This i n vitro phenomena i s thought t o b e a n expres- sion o f a basic cellular mechanism involved i n processes including wound healing, maintenance o f cellular organiza- tion i n tissues, surveillance f o r invading organisms, a n d development o f t h e early embryo (1). Several recent studies have reported a link between t h e metastatic behavior o f cancer cells a n d their motility i n culture (2-4). Such corre- lations will b e o f significance both i n understanding t h e metastatic process a n d i n devising clinical measurements fo r prognosis a n d treatment o f cancer. T he detection o f cell motility, however, h a s been a difficult a n d time consuming process. T h e simplest a n d most direct approaches involve microscopic observations o f cells, usually with t h e a i d o f time lapse cameras. In recent years, these data a r e often image processed a n d analyzed b y computer. This provides a direct measure o f translation a n d other aspects o f cell motion, b ut t h e procedure requires processing large volumes o f data. I n this paper, we describe a n d analyze a means to electri- cally detect cell motion i n tissue culture (5-7). I n this method, cells a r e cultured o n small gold electrodes evaporated on the bottom of standard culture dishes a n th e system's impedance i s followed with time. A s t h e cells attach a n d spread on t h e electrode surface, they alter th e effective area available f o r current flow causing as much as a n 8-fold increase i n t h e impedance o f th e system. After these initial changes, t h e impedance with time. In th e past, we have shown that these fluctuations i n impedance result from t h e motion o f cells on th e electrode. F o r example, treatment o f fibroblasts with 1 0 g M cytocha- lasin B resulted i n a nearly complete cessation o f t h e imped- ance fluctuations (7). The mechanism involved seemed a t first sight straightforward; a s cells move o n a n d o f f a n electrode, th e effective open area changes a n d with i t th e MATERIALS AND METHODS Tissue Culture. T he fibroblast cell lines WI-38 a n d WI-38 VA13 were obtained from the American Type Culture Col- lection. A l l culturing w a s done under standard conditions o f 370C a n d 5 % C02/95% air in Dulbecco's modified Eagle's medium (GIBCO) with 1 0 o fetal bovine serum (GIBCO) a n d antibiotics. Electrode Fabrication. T h e preparation o f 60-mm polysty- rene culture dishes containing gold electrodes deposited b y vacuum evaporation h a s been described ( 6 , 7 ) . Each finished dish contained on e large ( - 2 cm2) a n d four small (_10-3 cm2) electrodes. Impedance Measurements. For impedance measurements, t h e electrode-containing dish w a s placed i n a n incubator a n d medium ( - 4 m l ) was added over t h e electrodes. T h e large electrode a n d o n e o f the small electrodes were connected t o a phase-sensitive lock-in amplifier, a n d a n ac signal wa s supplied through a 1-Mfl resistor (see Fig. 1). The measure- ment w a s generally made with a 4000-Hz a c source with a n amplitude o f 1 . 0 V . F o r frequencies scans shown i n Fig. 3 , however, t he following a c frequencies a n d respective ampli- tudes were used: 2 2 H z a n d 0.014 V , 4 4 H z a n d 0.020 V , 8 8 H z a n d 0.027 V, 1 7 6 H z a n d 0.038 V , 3 5 2 H z a n d 0.054 V, 7 0 4 H z an d 0.075 V , 1408 H z a n d 0.105 , 2816 H z a n d 0.148 V , 5632 H a n d 0.207 V , 11,264 H z a n d 0.289 V , 22,528 H z a n d 0.405 V , 45,056 H z a n d 0.557 V , 90,112 H z an d 0.794 V. A l l connections were with coaxial cable t o minimize a ny background noise. F o r cell measurements, the dish w a s inoculated with 2 m l o f a cell suspension giving a concentra- tion o f 1 x 1 0 5 cells p e r cm 2 o f available area. Cells were allowed t o attach a n d spread f o r a t least 24 hr before t h e impedance measurements reported inthis paper were taken. RESULTS A N D DISCUSSION Fig. 1 shows a schematic o f the electrodes a n d t h e basic electrical setup used i n these measurements. In this two- 7896 T he publication costs o f this article were defrayed i n part b y page charge payment. This article must therefore b e hereby marked "advertisement" i n accordance with 18 U.S.C. §1734 solely to indicate this fact.
Transcript
8/8/2019 Micro Motion of Mammalian Cells Measured Electrically
P r o c . N a i l . A c a d . S c i . USAV o l . 8 8 , p p . 7 8 % - 7 9 0 0 , S e p t e m b e r 1 9 9 1C e l l B i o l o g y
M i c r o m o t i o n o f m a m m a l i a n c e l l s m e a s u r e d e l e c t r i c a l l y( c e l l m o t i l i t y / f i b r o b l a s t b e h a v i o r / n a n o m e t e r m o t i o n s / e l e c t r i c a l m e a s u r e m e n t s )
I V A R G I A E V E R AND C H A R L E S R . KEESE
S c h o o l o f S c i e n c e , R e n s s e l a e r P o l y t e c h n i c I n s t i t u t e , T r o y , NY 1 2 1 8 0 - 3 5 9 0
C o n t r i b u t e d b y I v a r G i a e v e r , May 1 6 , 1 9 9 1
ABSTRACT M o t i l i t y i s a f u n d a m e n t a l p r o p e r t y o f mam-m a l i a n c e l l s t h a t n o r m a l l y i s o b s e r v e d i n t i s s u e c u l t u r e b y t i m el a p s e m i c r o s c o p y w h e r e r e s o l u t i o n i s l i m i t e d b y t h e w a v e l e n g t ho f l i g h t . T h i s p a p e r e x a m i n e s a p o w e r f u l e l e c t r i c a l t e c h n i q u e b yw h i c h c e l l m o t i o n i s q u a n t i t a t i v e l y m e a s u r e d a t t h e n a n o m e t e rl e v e l . I n t h i s m e t h o d , t h e c e l l s a r e c u l t u r e d o n s m a l l e v a p o r a t e dg o l d e l e c t r o d e s c a r r y i n g w e a k a c c u r r e n t s . A l a r g e c h a n g e i nt h e m e a s u r e d e l e c t r i c a l i m p e d a n c e o f t h e e l e c t r o d e s i s o b s e r v e dw h e n c e l l s a t t a c h a n d s p r e a d o n t h e s e e l e c t r o d e s . When t h ei m p e d a n c e i s t r a c k e d a s a f u n c t i o n o f t i m e , f l u c t u a t i o n s a r eo b s e r v e d t h a t a r e a d i r e c t m e a s u r e o f c e l l m o t i o n . S u r p r i s i n g l y ,
t h e s e f l u c t u a t i o n s c o n t i n u e e v e n w h e n t h e c e l l l a y e r b e c o m e sc o n f l u e n t . B y c o m p a r i n g t h e m e a s u r e d i m p e d a n c e w i t h at h e o r e t i c a l m o d e l , i t i s c l e a r t h a t u n d e r t h e s e c i r c u m s t a n c e s t h ea v e r a g e m o t i o n s o f t h e c e l l l a y e r o f 1 n m c a n b e i n f e r r e d f r o mt h e m e a s u r e m e n t s . W e r e f e r t o t h i s a s p e c t o f c e l l m o t i l i t y a sm i c r o m o t i o n .
e l e c t r o d e i m p e d a n c e . T h e i m p e d a n c e f l u c t u a t i o n s , h o w e v e r ,c o n t i n u e a s c e l l l a y e r s b e c o m e c o n f l u e n t . To u n d e r s t a n dt h e s e r e s u l t s a n d t h e p o s s i b l e s o u r c e s o f t h e f l u c t u a t i o n s , weh a v e c o n s i d e r e d t h e i n t e r a c t i o n o f c u l t u r e d c e l l s w i t h t h ee l e c t r o d e s u r f a c e i n d e t a i l .
I t i s w e l l k n o w n f r o m i n t e r f e r e n c e r e f l e c t i o n m i c r o s c o p ys t u d i e s t h a t c e l l s i n c u l t u r e a t t a c h t o t h e s u b s t r a t u m b y s m a l lf o o t - l i k e p r o j e c t i o n s l e a v i n g s p a c e s o r c h a n n e l s b e t w e e n t h ev e n t r a l s i d e o f t h e c e l l a n d t h e s u b s t r a t u m ( 8 ) . T h e a m o u n t o fc u r r e n t f l o w i n g i n t h e s e c h a n n e l s , a n d h e n c e t h e i m p e d a n c eo f t h e c e l l - c o v e r e d e l e c t r o d e , w i l l d e p e n d o n t h e a p p l i e d a c
f r e q u e n c y . W e h a v e m o d e l e d t h i s s y s t e m a n d c o m p a r e d t h ec a l c u l a t e d i m p e d a n c e v a l u e s a s a f u n c t i o n o f f r e q u e n c y w i t ht h o s e m e a s u r e d f o r c o n f l u e n t l a y e r s o f W I - 3 8 a n d W I - 3 8VA13 c e l l s . I n a d d i t i o n , we h a v e c a l c u l a t e d t o w h a t d e g r e ec h a n g e s i n v a r i o u s c e l l p a r a m e t e r s w i l l a f f e c t i m p e d a n c em e a s u r e m e n t s .
L o c o m o t i o n o f c e l l s i n t i s s u e c u l t u r e h a s b e e n w i d e l y o b -s e r v e d , a s many m e t a z o a n c e l l s h a v e t h e a b i l i t y t o c r a w l u p o ns u r f a c e s . T h i s i n v i t r o p h e n o m e n a i s t h o u g h t t o b e a n e x p r e s -s i o n o f a b a s i c c e l l u l a r m e c h a n i s m i n v o l v e d i n p r o c e s s e si n c l u d i n g w o u n d h e a l i n g , m a i n t e n a n c e o f c e l l u l a r o r g a n i z a -t i o n i n t i s s u e s , s u r v e i l l a n c e f o r i n v a d i n g o r g a n i s m s , a n dd e v e l o p m e n t o f t h e e a r l y e m b r y o ( 1 ) . S e v e r a l r e c e n t s t u d i e sh a v e r e p o r t e d a l i n k b e t w e e n t h e m e t a s t a t i c b e h a v i o r o f
c a n c e r c e l l s a n d t h e i r m o t i l i t y i n c u l t u r e ( 2 - 4 ) . S u c h c o r r e -l a t i o n s w i l l b e o f s i g n i f i c a n c e b o t h i n u n d e r s t a n d i n g t h em e t a s t a t i c p r o c e s s a n d i n d e v i s i n g c l i n i c a l m e a s u r e m e n t s f o rp r o g n o s i s a n d t r e a t m e n t o f c a n c e r . T h e d e t e c t i o n o f c e l lm o t i l i t y , h o w e v e r , h a s b e e n a d i f f i c u l t a n d t i m e c o n s u m i n gp r o c e s s . T h e s i m p l e s t a n d m o s t d i r e c t a p p r o a c h e s i n v o l v em i c r o s c o p i c o b s e r v a t i o n s o f c e l l s , u s u a l l y w i t h t h e a i d o f t i m el a p s e c a m e r a s . I n r e c e n t y e a r s , t h e s e d a t a a r e o f t e n i m a g ep r o c e s s e d a n d a n a l y z e d b y c o m p u t e r . T h i s p r o v i d e s a d i r e c tm e a s u r e o f t r a n s l a t i o n a n d o t h e r a s p e c t s o f c e l l m o t i o n , b u tt h e p r o c e d u r e r e q u i r e s p r o c e s s i n g l a r g e v o l u m e s o f d a t a .
I n t h i s p a p e r , we d e s c r i b e a n d a n a l y z e a m e a n s t o e l e c t r i -c a l l y d e t e c t c e l l m o t i o n i n t i s s u e c u l t u r e ( 5 - 7 ) . I n t h i s m e t h o d ,c e l l s a r e c u l t u r e d o n s m a l l g o l d e l e c t r o d e s e v a p o r a t e d o n t h eb o t t o m o f s ta nd a r d t i s s u e c u l t u r e d i s h e s a n d t h e s y s t e m ' s
i m p e d a n c e i s f o l l o w e d w i t h t i m e . A s t h e c e l l s a t t a c h a n ds p r e a d o n t h e e l e c t r o d e s u r f a c e , t h e y a l t e r t h e e f f e c t i v e a r e aa v a i l a b l e f o r c u r r e n t f l o w c a u s i n g a s much a s a n 8 - f o l di n c r e a s e i n t h e i m p e d a n c e o f t h e s y s t e m . A f t e r t h e s e i n i t i a lc h a n g e s , t h e i m p e d a n c e f l u c t u a t e s w i t h t i m e .
I n t h e p a s t , we h a v e s h o w n t h a t t h e s e f l u c t u a t i o n s i ni m p e d a n c e r e s u l t f r o m t h e m o t i o n o f c e l l s o n t h e e l e c t r o d e .F o r e x a m p l e , t r e a t m e n t o f f i b r o b l a s t s w i t h 1 0 gM c y t o c h a -l a s i n B r e s u l t e d i n a n e a r l y c o m p l e t e c e s s a t i o n o f t h e i m p e d -a n c e f l u c t u a t i o n s ( 7 ) . T h e m e c h a n i s m i n v o l v e d s e e m e d a tf i r s t s i g h t s t r a i g h t f o r w a r d ; a s c e l l s move o n a n d o f f a ne l e c t r o d e , t h e e f f e c t i v e o p e n a r e a c h a n g e s a n d w i t h i t t h e
MATERIALS AND METHODS
T i s s u e C u l t u r e . T h e f i b r o b l a s t c e l l l i n e s W I - 3 8 a n d W I - 3 8VA13 w e r e o b t a i n e d f r o m t h e A m e r i c a n T y p e C u l t u r e C o l -l e c t i o n . A l l c u l t u r i n g w a s d o n e u n d e r s t a n d a r d c o n d i t i o n s o f
3 7 0 C a n d 5% C 0 2 / 9 5 % a i r i n D u l b e c c o ' s m o d i f i e d E a g l e ' sm e d i u m ( G I B C O ) w i t h 10o f e t a l b o v i n e s e r u m ( G I B C O ) a n da n t i b i o t i c s .
E l e c t r o d e F a b r i c a t i o n . T h e p r e p a r a t i o n o f 60-mm p o l y s t y -r e n e c u l t u r e d i s h e s c o n t a i n i n g g o l d e l e c t r o d e s d e p o s i t e d b yv a c u u m e v a p o r a t i o n h a s b e e n d e s c r i b e d ( 6 , 7 ) . E a c h f i n i s h e dd i s h c o n t a i n e d o n e l a r g e ( - 2 c m 2 ) a n d f o u r s m a l l ( _ 1 0 - 3 c m 2 )e l e c t r o d e s .
I m p e d a n c e M e a s ur e m e nt s . F o r i m p e d a n c e m e a s u r e m e n t s ,t h e e l e c t r o d e - c o n t a i n i n g d i s h w a s p l a c e d i n a n i n c u b a t o r a n dm e d i u m ( - 4 m l ) w a s a d d e d o v e r t h e e l e c t r o d e s . T h e l a r g ee l e c t r o d e a n d o n e o f t h e s m a l l e l e c t r o d e s w e r e c o n n e c t e d t oa p h a s e - s e n s i t i v e l o c k - i n a m p l i f i e r , a n d a n a c s i g n a l wa ss u p p l i e d t h r o u g h a 1 - M f l r e s i s t o r ( s e e F i g . 1 ) . T h e m e a s u r e -m e n t w a s g e n e r a l l y m a d e w i t h a 4 0 0 0 - H z a c s o u r c e w i t h a na m p l i t u d e o f 1 . 0 V . F o r f r e q u e n c i e s s c a n s s h o w n i n F i g . 3 ,h o w e v e r , t h e f o l l o w i n g a c f r e q u e n c i e s a n d r e s p e c t i v e a m p l i -t u d e s w e r e u s e d : 2 2 Hz a n d 0 . 0 1 4 V , 4 4 Hz a n d 0 . 0 2 0 V , 8 8
Hz a n d 0 . 0 2 7 V , 1 7 6 Hz a n d 0 . 0 3 8 V , 3 5 2 Hz a n d 0 . 0 5 4 V , 7 0 4Hz a n d 0 . 0 7 5 V , 1 4 0 8 Hz a n d 0 . 1 0 5 V , 2 8 1 6 Hz a n d 0 . 1 4 8 V ,5 6 3 2 Hz a n d 0 . 2 0 7 V , 1 1 , 2 6 4 Hz a n d 0 . 2 8 9 V , 2 2 , 5 2 8 Hz a n d0 . 4 0 5 V , 4 5 , 0 5 6 Hz a n d 0 . 5 5 7 V , 9 0 , 1 1 2 Hz a n d 0 . 7 9 4 V .
A l l c o n n e c t i o n s w e r e w i t h c o a x i a l c a b l e t o m i n i m i z e a n yb a c k g r o u n d n o i s e . F o r c e l l m e a s u r e m e n t s , t h e d i s h w a si n o c u l a t e d w i t h 2 m l o f a c e l l s u s p e n s i o n g i v i n g a c o n c e n t r a -t i o n o f 1 x 1 0 5 c e l l s p e r c m 2 o f a v a i l a b l e a r e a . C e l l s w e r ea l l o w e d t o a t t a c h a n d s p r e a d f o r a t l e a s t 2 4 h r b ef o r e t h ei m p e d a n c e m e a s u r e m e n t s r e p o r t e d i n t h i s p a p e r w e r e t a k e n .
RESULTS AND DISCUSSION
F i g . 1 s h o w s a s c h e m a t i c o f t h e e l e c t r o d e s a n d t h e b a s i ce l e c t r i c a l s e t u p u s e d i n t h e s e m e a s u r e m e n t s . I n t h i s t w o -
7 8 9 6
T h e p u b l i c a t i o n c o s t s o f t h i s a r t i c l e w e r e d e f r a y e d i n p a r t b y p a g e c h a r g ep a y m e n t . T h i s a r t i c l e m u s t t h e r e f o r e b e h e r e b y m a r k e d " a d v e r t i s e m e n t "i n a c c o r d a n c e w i t h 1 8 U . S . C . § 1 7 3 4 s o l e l y t o i n d i c a t e t h i s f a c t .
8/8/2019 Micro Motion of Mammalian Cells Measured Electrically
P r o c . N a t l . A c a d . S c i . USA 8 8 ( 1 9 9 1 ) 7 8 9 7
_- T I S S U E CULTURE M E D I U M( E L E C T R O L Y T E )
- CELLS
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F I G . 1 . S c h e m a t i c o f t h e e x -p e r i m e n t . I m p e d a n c e o f t h e s m a l le l e c t r o d e i s m e a s u r e d w i t h a
l o c k - i n a m p l i f i e r i n s e r i e s w i t h a1 - M f l r e s i s t o r t o o b t a i n a n a p p r o x -i m a t e c o n s t a n t c ur r e n t s o u r c e .T h e m e a s u r e d f l u c t u a t i o n s i n t h er e a l a n d i m a g i n a r y v o l t a g e a r e d i s -p l a y e d f o r a 1 - h r e x p e r i m e n t w i t hc o n f l u e n t W I - 3 8 VA13 f i b r o b l a s t su s i n g a 4 - k H z 1 - V s o u r c e . T h ei n - p h a s e a n d o u t - o f - p h a s e v o l t a g ev a l u e s a r e a p p r o x i m a t e l y p r o p o r -t i o n a l t o t h e r e s p e c t i v e c h a n g e s i nr e s i s t a n c e a n d c a p a c i t i v e r e a c -t a n c e o f a s e r i e s RC c i r c u i t .
p r o b e m e a s u r e m e n t , t h e r e s i s t a n c e o f t h e b u l k t i s s u e c u l t u r emedium i s i n s e r i e s w i t h t h e i m p e d a n c e o f t h e e l e c t r o d e s a n d
w i l l d o m i n a t e t h e measurement e x c e p t w h e n a n e l e c t r o d e i ss m a l l . T h e s o l u t i o n r e s i s t a n c e w i l l t h e n m a n i f e s t i t s e l f as a
s p r e a d i n g o r c o n s t r i c t i o n r e s i s t a n c e t h a t d e p e n d s o n t h e s i z eo f t h e e l e c t r o d e . As a n e x a m p l e , f o r a c i r c u l a r d i s k e l e c t r o d ei n a c o n d u c t i n g medium o f i n f i n i t e e x t e n t , t h e c o n s t r i c t i o nr e s i s t a n c e v a r i e s as p / 2 d , w h e r e p i s t h e r e s i s t i v i t y o f t h emedium a n d d i s t h e d i a m e t e r o f t h e e l e c t r o d e ( 9 ) . S i n c e t h ei m p e d a n c e a s s o c i a t e d w i t h t h e e l e c t r o d e - e l e c t r o l y t e i n t e r -f a c e must b e p r o p o r t i o n a l t o t h e i n v e r s e o f t h e a rea o f t h ee l e c t r o d e , 4 / i r d 2 , i t c a n a l w a y s b e m a d e t o d o m i n a t e t h e
c o n s t r i c t i o n r e s i s t a n c e b y m a k i n g t h e d i a m e t e r s u f f i c i e n t l ys m a l l . A t 4 kHz w i t h a n e l e c t r o d e o f - 1 0 - c m2, t h e r e a l p a r t
o f t h e i m p e d a n c e o f t h e e l e c t r o d e , t h e f a r a d a i c r e s i s t a n c e , i ss e v e r a l t i m e s l a r g e r t h a n t h e c o n s t r i c t i o n r e s i s t a n c e . U n d e rt h e s e c o n d i t i o n s , t h e a c t i v i t i e s o f a n c h o r e d c e l l s are c l e a r l y
r e v e a l e d . I f i n s t e a d two l a r g e e l e c t r o d e s h a d b e e n u s e d , t h e
s o l u t i o n r e s i s t a n c e w o u l d h a v e m a s k e d t h e m e a s u r e m e n t ,
a n d t h e presence o f c e l l s w o u l d b e b a r e l y d e t e c t a b l e . T h e
l o w e r p o r t i o n o f F i g . 1 s h o w s m e a s u r e d f l u c t u a t i o n s i n b o t ht h e i n - p h a s e a n d o u t - o f - p h a s e v o l t a g e as a f u n c t i o n o f t i m e f o re l e c t r o d e s c o v e r e d w i t h a c o n f l u e n t l a y e r o f W I - 3 8 VA13c e l l s .
T h e m o d e l u s e d t o c a l c u l a t e t h e s p e c i f i c i m p e d a n c e ( t h ei m p e d a n c e f o r a u n i t a r e a ) o f a c e l l - c o v e r e d e l e c t r o de as a
f u n c t i o n o f t h e f r e q u e n c y , I ' , i s s h o w n i n F i g . 2 . I t i s b a s e d o n
t h e m e a s u r e d s p e c i f i c i m p e d a n c e , Z n ( l ) , o f a c e l l - f r e e e l e c -t r o d e , t h e s p e c i f i c i m p e d a n c e , Z m ( V ) , t h r o u g h t h e c e l l l a y e r( i . e . , m a i n l y t h e c a p a c i t a n c e o f t h e u p p e r a n d lower c e l lm e m b r a n e s i n - s e r i e s ) a n d t h e r e s i s t i v i t y , p, o f t h e t i s s u ec u l t u r e m e d i u m . Th e c e l l s h a v e b e e n a p p r o x i m a t e d as c i r -c u l a r d i s k s ( n o t a l i m i t i n g a p p r o x i m a t i o n ) o f r a d i u s r c . Weh a v e a s s u m e d t h a t t h e c u r r e n t f l o w s r a d i a l l y i n t h e space
f o r m e d b e t w e e n t h e v e n t r a l s u r f a c e o f t h e c e l l a n d t h e
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F I G . 2 . D i a g r a m o f t h e c e l l s i n t i s s u e c u l t u r e e m p h a s i z i n g t h espaces b e t w e e n t h e c e l l a n d t h e s u b st r a t u m . C a l c u l a t e d r e s i s t a n c e i sd u e t o t h e c u r r e n t f l o w u n d e r t h e c e l l s a n d a n a d d i t i o n a l r e s i s t a n c eb e c a u s e t h e c u r r e n t must f l o w o u t b e t w e e n t h e c e l l s . B r o k e n l i n er e p r e s e n t s c a p a c i t i v e c u r r e n t f l o w t h r o u g h t h e c e l l m e m b r a n e s . T h ec e l l s ar e r e g a r d e d as d i s k s h a p e d when v i e w e d f r o m t h e t o p . T h e
s c h e m a t i c s i d e v i e w d i a g r a m o f c e l l s i s u s e f u l i n c o n s t r u c t i n g t h ed i f f e r e n t i a l e q u a t i o n s . H e r e p i s t h e r e s i s t i v i t y o f t h e s o l u t i o n , Z . ( v )i s t h e s p e c i f i c i m p e d a n c e o f t h e e l e c t r o d e - e l e c t r o l y t e i n t e r f a c e , a n d
Z m ( v ) i s t h e s p e c i f i c membrane i m p e d a n c e o f t h e c e l l s . If t h e
c a p a c i t a n c e o f a s i n g l e c e l l m e m b r a n e i s C , t h e n f o r t h e i n t a c t c e l l ,Zm = - i / 2 i r v ( C / 2 ) . I n a l l c a l c u l a t i o n s C i s s e t a t 1 A F / c m 2 .
n o t c h a n g e i n t h e z d i r e c t i o n . T h e e q u a t i o n s i n F i g . 2 c an b e
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p o t e n t i a l m e a s u r e d i n t h e s o l u t i o n j u s t o u t s i d e t h e c e l l l a y e r ,a n d h i s t h e h e i g h t o f t h e space b e t w e e n t h e v e n t r a l s u r f a c e
o f t h e c e l l a n d t h e s u b s t r a t u m .
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f u n c t i o n s o f f i r s t a n d s e c o n d k i n d ( 1 0 ) . By u s i n g p r o p e r
b o u n d a r y c o n d i t i o n s , t h e s p e c i f i c i m p e d a n c e f o r a c e l l -c o v e r e d e l e c t r o d e c a n b e w r i t t e n a s f o l l o w s :
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o f o r d e r 0 a n d 1 , a n d i i s V.T h e a n s w e r i s r a t h e r i n v o l v e d
b u t s t r a i g h t f o r w a r d t o d e v e l o p ; a d e t a i l e d d e r i v a t i o n w i l l b e
p u b l i s h e d e l s e w h e r e . N o t e t h a t t h e s o l u t i o n d e p e n d s o n t w op a r a m e t e r s - R b , t h e r e s i s t a n c e b e t w e e n t h e c e l l s f o r a u n i ta r e a , a n d a d e f i n e d b y :
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S i n c e Z n ( v ) i s m e a s u r e d a n d Z m ( v ) i s b a s i c a l l y t h e i m p e d a n c eo f t w o c e l l m e m b r a n e s i n s e r i e s ( s e e F i g . 2 ) , a a n d R b a r e t h eo n l y a d j u s t a b l e p a r a m e t e r s i n t h e p r e c e d i n g e x p r e s s i o n . T h e
f r e q u e n c y d e p e n d e n c e d o e s n o t a p p e a r e x p l i c i t l y i n t h ee q u a t i o n , a s i t i s c o n t a i n e d i n t h e i m p e d a n c e s Z n ( v ) a n d Z m ( v ) .
U s i n g t h i s m o d e l t o c a l c u l a t e t h e i m p e d a n c e o f a n e l e c t r o d es u p p o r t i n g a c o n f l u e n t l a y e r o f c e l l s , Z c , we f i r s t m e a s u r e t h ei m p e d a n c e o f a c e l l - f r e e e l e c t r o d e a t d i f f e r e n t f r e q u e n c i e s . I ti s c o n v e n i e n t t o i n t e r p r e t t h e m e a s u r e d s a m p l e i m p e d a n c e a se q u i v a l e n t t o t h a t o f a c a p a c i t o r a n d a r e s i s t o r i n s e r i e s a s w a sf i r s t d o n e b y W a r b u r g ( 1 1 , 1 2 ) f o r e l e c t r o l y t i c i n t e r f a c e s . T h i s
h a s b e e n d o n e f o r t h e r e s u l t s s h o w n i n F i g . 3 A a n d B . S i n c e
t h e c o n s t r i c t i o n r e s i s t a n c e i s i n s e r i e s w i t h t h i s i m p e d a n c e , i tc a n s i m p l y b e s u b t r a c t e d f r o m t h e t o t a l r e s i s t a n c e t o o b t a i nt h e r e a l r e s i s t i v e v a l u e o f Z n . A f t e r c a l c u l a t i n g Z c , t h ec o n s t r i c t i o n r e s i s t a n c e i s a d d e d b a c k f o r c o m p a r i s o n w i t h t h ee x p e r i m e n t a l r e s u l t s . T h e s o l i d l i n e s i n F i g . 3 C a n d D d i s p l a yt h e n o r m a l i z e d r e s i s t a n c e a n d c a p a c i t a n c e o b t a i n e d f r o m
e l e c t r o d e s c o n f l u e n tw i t h W I - 3 8
VA13a n d W I - 3 8
c e l l s b yd i v i d i n g w i t h t h e c o r r e s p o n d i n g q u a n t i t i e s f o r t h e c e l l - f r e ee l e c t r o d e s . T h e p o i n t s f o r a l l p a n e l s i n F i g . 3 a r e c a l c u l a t e dv a l u e s b a s e d o n t h e m o d e l .
T h e b e s t f i t t o t h e W I - 3 8 VA13 d a t a i s o b t a i n e d w i t h a =7 o h m l / 2 _ c m ( n o t e ' y r , i s u n i t l e s s ) a n d R b = 1 . 1 o h m - c m 2. B o t ht h e a v e r a g e r a d i u s o f t h e c e l l s ( 1 1 A m ) a n d t h e r e s i s t a n c e o f
t h e t i s s u e c u l t u r e m e d i u m ( 5 4 o h m - c m ) w e r e o b t a i n e d f r o m
i n d e p e n d e n t m e a s u r e m e n t s ( d a t a n o t s h o w n ) . T h i s g i v e s a n
a v e r a g e c a l c u l a t e d c h a n n e l h e i g h t ( s u b s t r a t u m t o v e n t r a l c e l ls u r f a c e ) o f 1 3 . 3 n m . T h e b e s t f i t f o r W I - 3 8 d a t a i s o b t a i n e dw i t h a = 3 . 5 o h m 1 / 2 _ c m a n d R b = 0 . 3 5 o h m - c m 2 . T h e s e n o r m a l
f i b r o b l a s t i c c e l l s a r e l a r g e r t h a n t h e t r a n s f o r m e d W I - 3 8 VA13
c e l l s , a n d b y u s i n g a n a v e r a g e m e a s u r e d r a d i u s o f 1 6 A u m , t h ea v e r a g e c a l c u l a t e d c h a n n e l h e i g h t b e c o m e s 1 1 3 n m . R a t h e r
t h a n m o d e l t h e c e l l s a s c i r c u l a r d i s k s , we c a n t r e a t t h e m a sr e c t a n g l e s w i t h w i d t h s e q u a l t o t h e d i a m e t e r u s e d . T h i s g i v e sl a r g e r v e n t r a l d i s t a n c e s o f 3 2 a n d 2 8 5 n m f o r W I - 3 8 VA13 a n d
W I - 3 8 , r e s p e c t i v e l y . T h e d i s t a n c e s i n b o t h c a s e s a r e i nr e a s o n a b l e a g r e e m e n t w i t h m e a s u r e m e n t s o b t a i n e d f r o mi n t e r f e r e n c e r e f l e c t i o n m i c r o s c o p y ( 1 3 ) b u t , a s c a n b e s e e n ,a r e s t r o n g l y d e p e n d e n t o n t h e a s s u m e d c e l l s h a p e . T h e
r e l a t i v e l y c l o s e p r o x i m i t y o f t h e t r a n s f o r m e d c e l l s t o t h es u b s t r a t u m c o m p a r e d w i t h t h e n o r m a l c e l l s i s , h o w e v e r ,i n d e p e n d e n t o f t h e c h o i c e o f c e l l s h a p e i n t h e m o d e l . T h e
r e s i s t a n c e o f t h e c e l l l a y e r u s e d t o f i t t h e d a t a i s o n l y on t h eo r d e r o f 1 o h m . c m 2 b u t n e v e r t h e l e s s i s n e e d e d t o g e t a g o o da g r e e m e n t w i t h t h e e x p e r i m e n t a l o b s e r v a t i o n s . T h i s s m a l lv a l u e e x p l a i n s w h y i t i s d i f f i c u l t b y c o n v e n t i o n a l m e a n s t om e a s u r e r e s i s t a n c e o f c e l l l a y e r s o t h e r t h a n e p i t h e l i a l c e l l s ,w h e r e t h e v a l u e i s - 2 o r d e r s o f m a g n i t u d e g r e a t e r ( 1 4 ) .
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8/8/2019 Micro Motion of Mammalian Cells Measured Electrically
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F I G . 3 . I m p e d a n c e as a f u n c t i o n o f f r e q u e n c y f o r a s m al l e l e c tr o d e o f a r e a 1 . 0 6 x 1 0 - 3 cm2. ( A ) R e s i s t a n c e o f a c e l l - f r e e e l e c t r o d e a n d t h e
same e l e c t r o d e c o n f l u e n t w i t h W I - 3 8 VA13 c e l l s . T h e p o i n t s ar e t h e c a l c u l a t e d v a l u e s . N o t e t h a t t h i s i s a l o g - l o g p l o t . ( B ) T h e same v a l u e s f o rt h e o b s e r v e d c a p a c i t a n c e . ( C ) F o r b e t t e r s e n s i t i v i t y t h e n o r m a l i z e d r e s i s t a n c e s ar e p l o t t e d , b o t h f o r an e l e c t r o d e c o n f l ue n t w i t h W I - 3 8 VA13
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e l e c t r o d e w i t h W I - 3 8 c e l l s . P o i n t s ar e c a l c u l a t e d v a l u e s ; o , W I - 3 8 V A 1 3 ; + , W I - 3 8 . ( D ) T h e same f o r n o r m a l i z e dc a p a c i t a n c e .
I t s h o u l d b e n o t e d t h a t t h e c e l l s , o f course, ar e n e i t h e rc i r c u l a r n o r r e c t a n g u l a r , n o r d o t h e y a l l h a v e t h e same s h a p e .T h i s s i m p l e m o d e l s h o w s , h o w e v e r , t h a t t h e c h a n g e i ni m p e d a n c e d u e t o a c o n f l u e n t c e l l l a y e r s t e m s f r o m two
s o urce s : t h e c u r r e n t f l o w b e t w e e n t h e v e n t r a l s u r f a c e o f
t h e c e l l s a n d t h e s u b s t r a t u m , a n d t h e r e s i s t a n c e b e t w e e nc e l l s .
F i g . 4A s h o w s t h e f i r s t 2 m i n o f d a t a t a k e n f r o m F i g . 1 . H e r et h e e q u i v a l e n t r e s i s t a n c e h a s b e e n c a l c u l a t e d f r o m t h e d a t a ,r e p r e s e n t i n g t h e s a m p l e as a r e s i s t o r a n d c a p a c i t o r i n s e r i e s ,a n d i s n o r m a l i z e d t o t h e v a l u e a t t i m e 0 . T h e s e ar e t y p i c a l o f
f l u c t u a t i o n s f r o m a n e l e c t r o d e w i t h c o n f l u e n t W I - 3 8 VA13
c e l l s m e a s u r e da t 4
k H z . F i g . 4B s h o w s t h e l a c k o f f l u c t u a -
t i o n s a f t e r a b r i e f 1 0 % o f o r m a l i n t r e a t m e n t t o k i l l t h e c e l l s . Th emeasurements h a v e b e e n o b t a i n e d w i t h a d i g i t a l l o c k - i na m p l i f i e r , a n d t h e d i g i t a l f e a t u r e a c c o u n t s f o r t h e s t e p s i n t h e
curve. A g a i n , s i n c e t h e e l e c t r o d e i s c o n f l u e n t w i t h c e l l s , t h e
m e a s u r e d f l u c t u a t i o n s i n t h e r e s i s t a n c e c a n n o t b e a s c r i b e d t o
v a r i a t i o n s i n t h e c e l l n u m b e r t h a t c o v e r t h e e l e c t r o d e as
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c u l t u r e s . I n s t e a d , t h e f l u c t u a t i o n s ar e d u e t o t h e v a r i a t i o n s i nt h e f a c t o r s t h a t make u p a, o r i n t h e r e s i s t a n c e b e t w e e n t h e
c e l l s , R b . Th e c a l c u l a t e d v a l u e s o f a o r R b t h a t c o r r e s p o n d t o
t h e e x p e r i m e n t a l r e s i s t a n c e c h a n g e s ar e s h o w n o n t h e r i g h th a n d o r d i n a n t o f F i g . 4 , a s s u m i n g t h a t e a c h i s e x c l u s i v e l y
r e s p o n s i b l e f o r t h e r e s i s t a n c e c h a n g e . A l s o m a r k e d o n F i g . 4
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F I G . 4 . Two m i nu t e s o f r e s i s t a n c e f l u c t u a t i o n s f o r l i v e ( A ) a n df o r m a l i n - t r e a t e d ( B ) W I - 3 8 VA13 c e l l s . T h e d i g i t a l a m p l i f i e r u s e da c c o u n t s f o r t h e s t e p s i n t h e curve. By c a l c u l a t i o n , i t c an b e s h o w nt h a t t h e s t e p h e i g h t i s c o n s i s t e n t w i t h a c h a n g e i n t h e average d i s t a n c eb e t w e e n t h e v e n t r a l s u r f a c e o f t h e c e l l s a n d t h e e l e c t r o d e s o f o n l y
0 . 0 1 nm o r a c h a n g e i n t h e c e l l r a d i u s o f 4 n m .
i s a b a r s h o w i n g t h e t y p i c a l c h a n g e i n t h e c a l c u l a t e d r e s i s -t a n c e t h a t w o u l d r e s u l t i f o n l y o n e o f t h e t h r e e v a r i a b l e s i n ah a d c h a n g e d b y t h e v a l u e l i s t e d . ( N o t e t h a t t h e c h a n g e i nr e s i s t a n c e i s n o t s t r i c t l y l i n e a r i n t h e s e v a l u e s . )
I t i s n o t c l e a r f r o m t h e s e r e s u l t s w h e t h e r t h e m e a s u r e dr e s i s t a n c e f l u c t u a t i o n s ar e d u e t o s m a l l v a r i a t i o n s i n a o r R b ;
h o w e v e r , f r o m p a r t i a l l y c o v e r e d e l e c t r o d e s , w h e r e R b must
b e 0 , i t c an b e e s t i m a t e d t h a t t h e y a r e o f r o ug h l y e q u a l
i m p o r t a n c e ( d a t a n o t s h o w n ) . What i s c l e a r , h o w e v e r , i s t h ee x q u i s i t e s e n s i t i v i t y o f t h e e x p e r i m e n t . I t s h o u l d b e n o t e dt h a t l a r g e f l u c t u a t i o n s i n t h e e l e c t r i c a l i m p e d a n c e c an b eo b s e r v e d w h e n , s i m u l t a n e o u s l y , n o d i s c e r n i b l e c h a n g e i ss e e n w i t h an o p t i c a l m i c r o s c o p e . T h i s i s n o t s u r p r i s i n gb e c a u s e c h a n g e s o f n a n o m e t e r s i n t h e c e l l d i a m e t e r o r
s u b n a n o m e t e r c h a n g e s i n t h e d i s t a n c e b e t w e e n t h e v e n t r a ls u r f a c e o f t h e c e l l a n d t h e s u b s t r a t e w i l l s i g n i f i c a n t l y a f f e c tt h e m e a s u r e d i m p e d a n c e . W e r e f e r t o t h i s s u b t l e a s p e c t o f c e l lm o t i l i t y as m i c r o m o t i o n . I t s h o u l d b e p o i n t e d o u t h e r e t h a t ,a t t h e p r e s e n t a m p l i f i e r m a g n i f i c a t i o n , t h e r e i s e s s e n t i a l l y n o
p r o b l e m w i t h e l e c t r i c a l n o i s e as c a n b e seen f r o m t h e f o r -m a l i n - t r e a t e d c e l l s . I t i s a l s o c l e a r t h a t t h e f l u c t u a t i o n s ar e
a s s o c i a t e d w i t h t h e l i v i n g c e l l s a n d i n n o way ar e a n a r t i f a c to f t h e m e a s u r e m e n t .
W h i l e t h e o r y a n d e x p e r i m e n t agree very w e l l , o n e s m a l l
d i f f i c u l t y s h o u l d b e p o i n t e d o u t . E x p e r i m e n t a l l y , t h e capac-
i t a n c e a t l o w f r e q u e n c y i n c r e a s e s f o r l o n g - t e r m ( a f e w d a y s )
e x p e r i m e n t s b y 5 - 1 0 % o f o r c o n f l u e n t e l e c t r o d e s . T h e i n c r e a s ev a r i e s a r b i t r a r i l y b e t w e e n e l e c t r o d e s i n a s i n g l e e x p e r i m e n ta n d f r o m e x p e r i m e n t t o e x p e r i m e n t . B e c a u s e t h e c e l l s f o r ma d h e s i o n p l a q u e s ( f o c a l c o n t a c t s ) w i t h t h e e l e c t r o d e s , t h em e a s u r e d c a p a c i t a n c e i s e x p e c t e d t o b e 5 - 1 0 % s m a l l e r t h a nt h a t f o r t h e c e l l - f r e e e l e c t r o d e . T h e r e a s o n f o r t h e i n c r e a s e i nc a p a c i t a n c e i s u n c l e a r b u t i t o f f e r s n o p r o b l e m f o r t h e t i m es c a l e o f t h e e x p e r i m e n t a l r e s u l t s d e s c r i b e d i n t h i s p a p e r .U n f o r t u n a t e l y , u n t i l t h i s p r o b l e m i s u n d e r s t o o d , t h e e x p e r i -m e n t a l m e t h o d c a n n o t b e u s e d
t om e a s u r e t h e
s i z e so f
t h ea d h e s i o n p l a q ue s b e t w e e n t h e c e l l s a n d t h e s u b s t r a t u m .
A c o n f l u e n t e l e c t r o d e c o n t a i n s o n t h e o r d e r o f 5 0 c e l l s ; i ti s , h o w e v e r , p o s s i b l e t o m e a s u r e t h e e f f e c t o f a s i n g l e c e l l o nt h e e l e c t r o d e . T h i s i s e x p e r i m e n t a l l y m o r e d i f f i c u l t . W e a r ea l s o e x a m i n i n g how v a r i o u s e x t e r n a l f a c t o r s , s u c h a s t e m -p e r a t u r e , p H , o r a d d i t i o n o f d r u g s w i l l a f f e c t t h e m o t i o n o fc e l l s a t t h i s l e n g t h s c a l e . T h e i n h e r e n t s i m p l i c i t y o f t h e s y s t e ma n d t h e s e n s i t i v i t y o f t h e s e m e a s u r e m e n t s o f f e r s g r e a t p r o m -i s e f o r m a n y t i s s u e c u l t u r e a p p l i c a t i o n s .
T h i s w o r k w a s c a r r i e d o u t i n p a r t p u r s u a n t t o a c o n t r a c t w i t h t h eN a t i o n a l F o u n d a t i o n f o r C a n c e r R e s e a r c h .
1 . A b e r c r o m b i e , M . ( 1 9 8 2 ) i n C e l l B e h a v i o r , e d s . B e l l a i r s , R . ,C u r t i s , A . & D u n n , G . ( C a m b r i d g e U n i v . P r e s s , L o n d o n ) , p p .
1 0 - 4 8 .2 . P a r t i n , A . W . , I s a a c , J . T . , T r e i g e r , B . & C o f f e y , D . S . ( 1 9 8 8 )C a n c e r R e s . 4 8 , 6 0 5 0 - 6 0 5 3 .
3 . P a r t i n , A . W . , S c h o e n i g e r , J . S . , M o h l e r , J . L . & C o f f e y , D . S .( 1 9 8 9 ) P r o c . N a t l . A c a d . S c i . USA 8 6 , 1 2 5 4 - 1 2 5 8 .
4 . B r a d y - K a l n a y , S . M . , S o i l , D . R . & B r a c k e n b u r y , R . ( 1 9 9 1 )I n t . J . C a n c e r 4 7 , 5 6 0 - 5 6 8 .
5 . G i a e v e r , I . & K e e s e , C . R . ( 1 9 8 9 ) P h y s i c a D 3 8 , 1 2 8 - 1 3 3 .6 . G i a e v e r , I . & K e e s e , C . R . ( 1 9 8 6 ) IEEE T r a n s . B i o m e d . E n g .
3 3 , 2 4 2 - 2 4 7 .
7 . G i a e v e r , I . & K e e s e , C . R . ( 1 9 8 4 ) P r o c . N a t l . A c a d . S c i . USA8 1 , 3 7 6 1 - 3 7 6 4 .
8 . H e a y s m a n , J . E . M . & P e g r u m , S . M. ( 1 9 8 2 ) i n C e l l B e h a v i o r ,e d s . B e l l a i r s , R . , C u r t i s , A . & D u n n , G . ( C a m b r i d g e U n i v .P r e s s , L o n d o n ) , p p . 4 9 - 7 6 .
9 . H o l m , R . ( 1 9 4 6 ) E l e c t r i c a l C o n t a c t s ( A l m q v i s t & W i k s e l l s ,U p p s a l a ) , p . 1 6 .
1 0 . H i l d e b r a n d , F . B . ( 1 9 4 8 ) A d v a n c e d C a l c u l u s f o r E n g i n e e r s( P r e n t i c e - H a l l , E n g l e w o o d C l i f f s , N J ) , p p . 1 5 2 - 1 8 1 .
1 1 . W a r b u r g , E . ( 1 9 0 1 ) A n n . P h y s . 6 , 1 2 5 - 1 3 5 .
1 2 . O n a r a l , B . , S u n , H . H . & S c h w a n , H . P . ( 1 9 8 4 ) IEEE T r a n s .
B i o m e d . E n g . 3 1 , 8 2 7 - 8 3 2 .
1 3 . I z z a r d , C . S . & L o c h n e r , L . R . ( 1 9 8 0 ) J . C e l l S c i . 4 2 , 8 1 - 1 1 6 .
1 4 . F u l l e r , S . , v o n B o n s d o r f f , C . H . & S i m o n s , K . ( 1 9 8 4 ) C e l l 3 8 ,6 5 - 7 7 .
A
J Ah A r c A P0 . 0 5 n m 2 0 n m 0 . 2 Q - c m
B
P r o c . N a t l . A c a d . S c i . USA 8 8 ( 1 9 9 1 )
