Supplementary Information

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1 Y Axis Title Y Axis Title Y Axis Title Real part of the polarization oeffiient for quadrupole, Re[ f (2) ] CM Supplementary Information ) Appendix A: Real part of the polarization oeffiient (Re[ f ]) for quadrupole of T lymphoytes, B lymphoytes, granuloytes, monoytes, SkBr, and ~ (2 CM T lymphoytes B lymphoytes 0. Granuloytes -0.2 Monoytes SkBr k 10 k k 110M M M 110G 9 Frequeny (Hz) 0.0 ~ Fig. S1 Calulated real part of the polarization oeffiient (Re[ f (2) T-ell T-ell0.0 T-ell CM ]) for quadrupole of B-ell 0.0 T-ell T-ell B-ell B-ell Granuloyte human leukoyte subpopulations [T lymphoyte ( ), T-ell B lymphoyte ( ), B-ell granuloyte -0.2Granuloyte B-ell Granuloyte Monoyte Monoyte B-ell Granuloyte ( ), Granuloyte and monoyte -0.2 ( )], Monoyte and metastati breast [SkBr ( )] SKBR and lung [ SKBR Granuloyte Monoyte -0.2 Monoyte SKBR ( )] aner ell lines, suspended in a 2.6 ms mmonoyte 1 low-ondutivity medium. SKBR The -0.SKBR SKBR measured 10 size and dieletri 10 properties 10of 5 the ells (Table ) were used 10 7 for this alulation X 10 5 Axis 10 Title s Title s Title X Axis Title X Axis Title X Axis Title 1

2 Appendix B: Point harge otupole model z +Q(-b,0,) Q(0,-b,) 2 Q(0,b,) Cell (0,0,z) +Q(-b,0,0) 1 2 Q(0,-b,0) +Q (b,0,) 2 2 b z Q(0,b,0) y 1 +Q (b,0,0) x Fig. S2 A point harge otupole model showing the loations of the eight point harges +Q at (±b, 0, 0) and (±b, 0, ) and Q at (0, ±b, 0) and (0, ±b, ). A ell of radius r is loated on the entral axis, the z-axis, of the otupole. For the point harge otupole model (Fig. S2), if the radius of the ell, r, is muh shorter than the distane between the enter of the ell and the point harges on the bottom, 2 2 b z, the z-diretional nqdep fore, ating on the ell on the entral axis of the otupole, generated from the four point harges at (±b, ±b, 0) on the bottom an be alulated using Eq. (). In the equation, the point harge, Q, is expressed as: Q 2 C V 2 C V (S1) ele rms ele p 2

3 where C ele is the total sum of the mutual apaitanes of an eletrode with respet to oppositely polarized eletrodes. V rms and V p are the root mean square voltage and the peak voltage of the nqdep signal, respetively. Using finite element analysis with ommerially available software, ANSYS (ANSYS In.), C ele of the ROT-mirohip used here was obtained as pf. For the peak voltages, V P, of the nqdep signals of 1.5 and 2 Vp, the harges, Q in Eq. (S1), indued on the eah eletrodes were alulated as C and C, respetively.

4 Appendix C: Eletrorotation (a) (b) t r ε yto, σ yto r ε, σ ε, σ ε m, σ m Fig. S (a) The single-shell dieletri model and (b) the equivalent homogeneous sphere model for a single ell. If a single-shell dieletri model (Fig. Sa) is modified as an equivalent homogeneous sphere (Fig. Sb), the effetive omplex permittivity, j / homogeneous sphere an be expressed as: 2 ~, of the equivalent ~ r ~ yto 2 r t ~ yto 2 ~ r yto r t ~ yto 2 (S2) where r and t are the outer radius and the brane thikness of the single-shell dieletri model, respetively. j / yto and j / yto yto are the omplex permittivities of the ytoplasm and brane of the single-shell dieletri model, respetively.

5 For the equivalent homogeneous sphere, the imaginary part of the Clausius Mossotti fator is m m Im 2 2, (S) mw 2 m 2 m 2 m f CM, where mw 1 mw 2 m m and m are the permittivity and ondutivity of medium, respetively. The area-speifi brane apaitane, C t, and ytoplasm ondutivity, yto, an be extrated / by minimization of the root mean square error between the measured ROT spetrum and the imaginary part of the Clausius Mossotti fator in Eq. (S). 5

6 PE PE PE PE Appendix D: Purity of leukoyte subpopulations 10 (a) T ell.001 T lymphoytes (99.%) 10 (b) B ell.001 B lymphoytes (99.%) R R1 R R FITC FL1-H G ell.001 () Granuloytes (9.9%) FITC FL1-H M ell.001 (d) Monoytes (99.%) 10 2 R1 R R R FL1-H FITC FL1-H FITC Fig. S FACS satter plots showing fluoresently labeled (a) T lymphoytes with anti-cd- FITC and red fluoresent nulei aid stain, (b) B lymphoytes with anti-cd20-pe and anti- CD5-FITC, () granuloytes with anti-cd66b-fitc and red fluoresent nulei aid stain, and (d) monoytes with anti-cd1-pe and anti-cd5-fitc. 6

7 Vertial Fore, F ver (10-12 N) Vertial Fore, F (10 ver (10-12 N) Appendix E: Theoretial analysis of the vertial fore ating on ells aording to the levitation height 5 SkBr Monoyte 2 Granuloyte T & B lymphoytes Levitation height, z (um) Bottom of Channel 1.0 Top Levitation height, z (um) Fig. S5 Theoretial analysis of the vertial fore ating on ells [Eq. (5)], whih is the sum of the nqdep fores generated from the top and bottom quadrupole eletrodes and the gravitation fore, for varying levitation heights along the entral axis of the D otode. 7

8 nqdep signals of 20 khz, 2 V peak and 1.5 V peak were applied to normal leukoytes and aner ells, respetively. For the ROT-mirohip with a mirohannel 60 µm in height, theoretial analysis showed that the ells suspended in 2.6 ms m 1 low-ondutivity medium were levitated to a height of approximately µm. The gravitation fore then pulls the ells down to approximately 9 15 µm from the middle of the mirohannel. 8

9 Levitation height (um) Appendix F: Theoretial analysis of the levitation heights of ells aording to the peak voltage of the nqdep signal SkBr Monoytes Granuloytes T & B lymphoytes Peak voltage of the nqdep signal (Vp) Fig. S6 Analyzed levitation heights of ells aording to the peak voltage of the nqdep signal of 20 khz. Condutivity of the medium was 2.6 ms m 1 and the mirohannel height of the ROT-mirohip was 60 µm. 9

10 Rotation speed (S -1 ) Appendix G: Rotation speed of a trapped T lymphoyte for 6 min Frist data Seond data Third data Time (min) Fig. S7 Rotation speed of a trapped T lymphoyte for 6 min. The T lymphoyte was trapped by a 20 khz, 2 Vp nqdep signal and rotated by a 100 khz, 0. Vp ROT signal. Referene 1. J. Z. Chen, A. A. Darhuber, S. M. Troian and S. Wagner, Lab on a Chip, 200,, T. B. Jones, Eletromehanis of Partiles, Cambridge University Press, T. Sun and H. Morgan, Mirofluidis and Nanofluidis, 2010, 8,