### Cells and media

NB4 cells from a leukemia cell line were cultured in RPMI-1640 medium (Invitrogen) supplemented with 10% fetal bovine serum (Gibco BRL) and 100 U/mL of penicillin–streptomycin (Sigma-Aldrich). DOX (Sigma-Aldrich) was used to alter the biological properties of NB4 cells, and NB4-DOX cells were cultured in 0.05 μM DOX medium for 96 h. All cells were cultured in a humidified incubator with 5% CO_{2} at 37 °C. To conduct DEP-based cell stretching experiments, the cells were resuspended in an isotonic buffer medium consisting of 8.5% sucrose, 0.3% dextrose, and 20 mg/L CaCl_{2} [37]. For confocal fluorescence imaging, the cells were fixed with 4% paraformaldehyde and permeabilized with 0.5% Triton X-100 for 10 min at room temperature; afterward, the actin cytoskeleton of NB4 cells was stained with rhodamine-phalloidin (Invitrogen) for 10 min.

### Experimental setup for DEP cell stretching

An experimental platform consisting of a function generator, a positioning table, an optical microscope unit, a syringe pump, and a computer system was set up for DEP-based cell stretching and manipulation experiments (Fig. 1). A microfluidic chip with integrated microelectrodes was placed on the positioning table for viewing under the optical microscope. Figure 2a, b show the design of the microfluidic chip. The microchannel has overall dimensions of 5000 μm by 50 μm, and cell containing medium was injected into the channel by the syringe pump. The integrated microelectrodes with a gap width of 20 μm (Fig. 2c) were patterned on an indium tin oxide (ITO)-coated glass slide by using photolithography. Details of the chip fabrication was presented in our earlier work [8].

To stretch the cells, the microfluidic chip was connected to a function generator to produce a non-uniform electric field in the microenvironment via a pair of electrodes. The frequency of the electric field was selected so that a net DEP force was applied on the cells to lead them toward the electric field maxima. Based on this principle, the cells were manipulated and captured by one of the two electrodes. Given that the conductivity of the medium *σ*
_{
m
} is lower than that of the cell cytoplasm *σ*
_{
c
} (i.e., *σ*
_{
m
} < *σ*
_{
c
}), the cells started to stretch and elongate along the electric field lines [38]. Finite element software COMSOL Multiphysics was used to simulate the distribution of electric field for computing the DEP force acting on the cells. The stretching experiment was completed within 30 min in order to minimize the threat to the survival of the cells [37].

### Experimental setup for OT cell stretching

An optical tweezers system (BioRyx 200) that can generate multiple optical traps was utilized to conduct the stretching experiments. Prior to the experiments, streptavidin-coated polystyrene beads with a radius of 1.55 μm were coated with biotin-conjugated concanavalin A at 4 °C for 40 min. The coated beads were then rinsed and incubated with the cells to enable attachment between the beads and the cells.

The cells were loaded on a glass slide and only cells with two beads attached on opposite sides of the diameter line were chosen for the experiments. One optical trap was used to hold one bead in place while one optical trap was used to manipulate the opposing bead until the bead escaped from the trap. The laser power used is 0.5, 1, 1.5, 2, 2.5 and 3 W, respectively, and details of the experiments can be referenced to the work in [9].

### Computation of DEP force

In this work, three different approaches were considered to estimate the DEP force acting on the cells. The first approach employs the widely adopted DEP force equation [39, 40]:

$$ F_{DEP} = 2\pi r^{3} \varepsilon_{0} \varepsilon \text{Re} \left[ {K(\omega )} \right]\nabla E^{2} $$

(1)

where *r* is the cell radius, which is approximately 7 μm for both NB4 and NB4-DOX cells as measured using ImageJ software; *ε*
_{
0
} is a dielectric constant of the vacuum, which is 8.854 × 10^{−12} F/m; *ε* is the relative dielectric constant of the DEP medium, which is 78; *E* is the electric field; and \( \nabla \) is the del (gradient) operator; Re[K(ω)] is the real part of the Clausius–Mossotti (CM) factor, which is dependent on the angular frequency (ω) of the applied potential, as well as the dielectric properties of the cell and the medium.

The expression above is based on the equivalent dipole moment (EDM) method used to derive the net force induced at the two poles of a polarized cell. To compute the force, the gradient of the square of an electric field, which is dependent on the geometry of microelectrodes, is required and this can be obtained through computer simulation [20, 41] or analytically using the boundary element method [42].

Alternatively, the DEP force can be calculated by integrating the Maxwell stress tensor (MST) over the surface of the cell to yield the force. For general tip-to-tip electrode configuration, Engelhardt et al. [23] proposed a simple approximation by assuming the electric field inside the cell is small as compared to the field outside, and the force can thus be estimated as [23]:

$$ F_{DEP} = \frac{1}{4}\varepsilon_{0} \varepsilon E^{2} A $$

(2)

where the electric field is *E* = *U*/*d*, in which *U* is the applied potential and *d* is the electrode gap (20 μm). *A* is the surface area of the cell. This rough approximation also neglects the effect of the applied frequency, which could lead to a change in the DEP force between positive and negative at various frequencies. For a better force estimation, Wang et al. [43] adopted the phasor representation for the electric field (E = E_{0}e^{iwt}) and the expression becomes [43, 44]:

$$ F_{DEP} = \frac{1}{4}\varepsilon_{0} \varepsilon \int\limits_{A} {\left( {EE^{*} + E^{*} E - \left| E \right|^{2} } \right)} \cdot \hat{n}dA $$

(3)

where *E** is the complex conjugate of the electric field and \( \overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{n} \) is the unit vector normal to A.

### Actin cytoskeleton modeling

We previously developed an actin microstructural model by using F-actin and ABPs to characterize the mechanical properties of cells [26]. In the model, actin filaments are randomly distributed to form the 3D actin cytoskeleton network and each filament is modeled to exhibit the nature of a semiflexible polymer. The ends of any two filaments are connected randomly by ABPs, which are represented by linear springs. Under cell stretching condition, the force acting on the *i*th vertex (*F*
_{
i
}) can be consisted of the internal forces of the actin filaments (*f*
_{
a
}) and the ABPs (*f*
_{
c
}) connected to the vertex, as well as the external stretching force (*f*
_{s}). Force balance was derived using the Newton’s equations of motion to determine the positions of all actin vertices; these equations are expressed as follows:

$$ m_{i} \ddot{r}_{i} + \eta \dot{r}_{i} = F_{i} $$

(4)

$$ F_{i} = \sum\limits_{i = 1}^{{n_{a} }} {f_{a\_i} } + \sum\limits_{i = 1}^{{n_{c} }} {f_{c\_i} + f_{s} } $$

(5)

where *r*
_{
i
} = [*x*
_{
i
}
*y*
_{
i
}
*z*
_{
i
}]^{T} denotes the position of the *i*th vertex of the actin network, *m*
_{
i
} is the fictitious mass of the *i*th vertex, *η* is the viscosity of the cytoplasm, *n*
_{
a
} is the number of actin filaments, and *n*
_{c} is the number of ABPs. Force-extension behavior of ABPs can be represented by linear Hookean springs with a stiffness of *k*
_{
c
}, and the force-extension behavior of actin filaments can be modeled using MacKintosh-derived WLC model, as follows [45]:

$$ f_{a} = \frac{{81k_{b} TL_{p}^{2} L_{c}^{2} (\Delta r + \delta r_{0} )}}{{(L_{c}^{2} - 6L_{p} \Delta r - 6L_{p} \delta r_{0} )^{2} (L_{c}^{2} + 3L_{p} \Delta r + 3L_{p} \delta r_{0} )}} $$

(6)

where Δ*r* is the extension of the actin filament, *δr*
_{
0
} is the pre-extension of the actin filament caused by prestress, *L*
_{
p
} is the persistence length, *L*
_{
c
} is the contour length, *k*
_{
b
} is the Boltzmann’s constant, and *T* is the absolute temperature. In addition, the relationship among contour length (*L*
_{
c
}), diameter of F-actin (*d*
_{
Actin
}), actin concentration (*C*
_{
AF
}), and density of the crosslinks (*R*) of actin network [45] can be expressed as follows:

$$ L_{c} = \frac{{R^{0.2} d_{Actin} }}{2}\sqrt {\frac{\pi }{{C_{AF} }}} $$

(7)

Through the model, the influence of parameters such as the actin concentration, density of cross-link, and the prestress effect on the actin cytoskeleton can be quantitatively analyzed.

### Experimental procedure

The structural parameters of the cell model were obtained through fitting of experimental data. NB4 and NB4-DOX cells were stretched under different DEP forces, and deformations were evaluated from the captured images. As discussed in Eq. (1), the strength of the DEP force is dependent on the size of the cell, the applied frequency, and the electric field gradients from the electrodes. The real part of the CM factor is a frequency dependent parameter that is bounded between −0.5 and 1 [40]. A typical biological cell can maintain a CM factor of around 1 in the mega-hertz frequency range. To select an appropriate operating frequency for a voltage input, a frequency range of 100 Hz to 5 MHz was examined to observe the movements of NB4 cells. At the maximum frequency of 5 MHz, the NB4 cells in a low-conductivity medium (5.29 mS/m) can still be manipulated and captured by one of the microelectrodes via positive DEP (pDEP) effect. However, when the frequency was gradually reduced to 25 kHz or lower, NB4 cells started to detach or repel from the microelectrode, indicating a switch from pDEP to negative DEP (nDEP) effect. This work used an operating frequency of 1 MHz, which can provide the maximal CM factor and minimize the Joule heating effect on the cells [24].

The NB4 cells were stretched to different scales by adjusting the strength of the electric field. An initial sinusoidal voltage input of 2 V_{pp} (peak-to-peak) was first applied to capture and immobilize the NB4 cells, and then the voltage amplitude was adjusted to 3, 4, 5, 6, 7, 8, and 9 V_{pp} to stretch the NB4 cells for 3 min. The same stretching experiments were performed for NB4-DOX cells. Figure 3a–d show the deformation of an NB4 cell, and Fig. 3e–h show the deformation of an NB4-DOX cell under different voltages. The deformation along the long axis of the ellipsoidal cell was measured using ImageJ software [19, 41].