Non-contact method for directing electrotaxis

We present a method to induce electric fields and drive electrotaxis (galvanotaxis) without the need for electrodes to be in contact with the media containing the cell cultures. We report experimental results using a modification of the transmembrane assay, demonstrating the hindrance of migration of breast cancer cells (SCP2) when an induced a.c. electric field is present in the appropriate direction (i.e. in the direction of migration). Of significance is that migration of these cells is hindered at electric field strengths many orders of magnitude (5 to 6) below those previously reported for d.c. electrotaxis, and even in the presence of a chemokine (SDF-1α) or a growth factor (EGF). Induced a.c. electric fields applied in the direction of migration are also shown to hinder motility of non-transformed human mammary epithelial cells (MCF10A) in the presence of the growth factor EGF. In addition, we also show how our method can be applied to other cell migration assays (scratch assay), and by changing the coil design and holder, that it is also compatible with commercially available multi-well culture plates.

surfaces so as to not distort any other part of the well. The part was then flame annealed to a point safe from cracking before finally being oven annealed, as described earlier.

Analysis of induced electric fields in modified transmembrane assay experiments
A time-dependent magnetic induction ( B t    ) must be present in order to induce an electric field in a non-contact manner. Such an induced electric field can be produced either by a constant magnitude magnetic field that is changing its direction versus time or by a magnetic field in a specific direction that is changing its magnitude with respect to time, or both. In this work, we have elected for the simplest approach which involves the latter. The 20 Vpp, 100 kHz sawtooth shaped voltage waveform (Fig. 2a) imposed on the previously described electromagnetic coil (Fig. 1a) results in a time-dependent current flow through it. The current through the coil varies in time both in magnitude and direction, and is a complicated function of the inductance and intrinsic capacitance of the coil as well as its coupling with the function generator. Consequently, the resulting magnetic induction in cylindrical coordinates, B(r,z, t)  , and associated vector potential A(r, z, t)  vary with time both in magnitude and direction, where r and z are the radial and axial coordinates measured from an origin located at one end of the coil along its centerline. The induced electric field E(r,z, t)  can then be calculated from the vector potential, A(r, z, t)  : The time-dependent current through the coil can be measured using a sense resistance (a smaller resistance) connected in series with the coil in the circuit, and by measuring the timedependent voltage drop across the 1.25 sense resistance (Supplementary Fig. S7). Extreme care must be taken so as to ensure that no stray capacitances arising for example from BNC connectors corrupt the measurement. One way to verify the measurement, is to connect the sense resistance upstream of the coil and ensure that the same current profile versus time is obtained as when the sense resistance is connected downstream of the coil. It is also important to point out that use of a sense resistance for current measurement is only reliable at low values of the duty cycle (on the order of tens of kHz or lower) because of the unknown intrinsic coil capacitance which is difficult to quantify at high values of the duty cycle (e.g. at 100 kHz) due to leakage.
We adopt the following methodology for calculating the induced electric fields relevant to our experiments. The current through the electromagnetic coil is measured for an imposed sawtooth voltage waveform of 20 Vpp at 1 kHz using a 1.25  sense resistance ( Supplementary  Fig. S7). A circuit element model (Supplementary Fig. S8) is then used to predict the current through the coil at 1 kHz, and validated against the current measurement using the sense resistance at 1 kHz. The model is used to infer the intrinsic coil capacitance ( Supplementary  Fig. S8), and then used to predict the coil conduction current for the experimental conditions where the imposed 20 Vpp sawtooth shaped voltage waveform is applied at 100 kHz. Once the time-varying current is calculated, the vector potential A(r, z, t)  is calculated using an analytical solution for the vector potential at a point given a circular current winding of a given diameter at a specific location R1 : , K(m j ) is the complete elliptic integral of the first kind R2 , E(m j ) is the complete elliptic integral of the second kind R2 , I is the current through winding j, a j is the radius of the j th winding, r is the radial coordinate, z is the axial coordinate (with the origin taken along the centerline of the coil and at one end of the coil), and A j is the contribution to the vector potential at (r,z) at time t due to current I(t) flowing in the j th winding. By taking the coil to be comprised of a perfectly stacked set of wire loops (windings) with different diameters and carrying the same current R3 , the vector potential at any point in space can be obtained as the superposition of the individual contributions from each loop of wire in the coil: where N is the total number of windings in the coil (35 layers x 159 windings per layer = 5565). Note that in Eq.(3) the only time dependent quantity is the current I. The radial and axial components of magnetic induction are then calculated from: and the induced electric field is given by: . Note that the induced electric field E  calculated from (6) varies with the radial coordinate r and axial coordinate z. For the case of rapidly changing transients, it is recommended that the derivative dI/dt in equation (6) be calculated using higher order accurate finite difference formulae such as a fourth-order accurate finite difference formula R4 . The current through the coil is measured using a sense resistance of 1.25  with the function generator supplying a 20 Vpp sawtooth waveform at 1 kHz (Supplementary Fig. S9). Also shown in the figure is the coil conduction current calculated using the circuit element model (Supplementary Fig. S8). The intrinsic coil capacitance was determined by parametric variation to be 30 nF using the measured values (at 1 kHz) of 50.45  for the d.c. resistance and 14.25 mH for the inductance. Varying the intrinsic coil capacitance alters the magnitude of the spike whereas the inductance and resistance together shift the bowl shaped profile for all other times in the period (Supplementary Fig. S9). As can be seen, the agreement between prediction and measurement is excellent. The circuit element model is used to predict the current at 100 kHz using the same values of inductance, resistance, and capacitance at 1 kHz. The resulting current as a function of time exhibits asymmetry over a period (Supplementary Fig. S10). The induced electric field is proportional to dI/dt (equation (6)) and is therefore also asymmetric over any given period (Fig.  2b).

Analysis of induced electric fields in visualization of actin filaments
For the purpose of visualizing actin filaments using phalloidin and fluorescence microscopy, the orientation of the coil has to be changed compared to the configuration used in the transmembrane assay experiments. The electromagnetic coil used to generate the induced electric fields in these experiments also consists of multiple windings (18 layers, ~ 67 turns per layer) of insulated 32 AWG (0.268 mm diameter with insulation or 0.202 mm diameter bare) wire. The inner diameter of the coil is 14.2 mm, the outer diameter is 2.332 cm, and its length is 2.47 cm. Measurements of the coil resistance and inductance using an LCR meter (Extech Instruments Model 380193) yielded 24.58 Ω and 12.17 mH, respectively, at 1 kHz. The coil is placed at the center of the holder with a standard 60 mm diameter culture plate on top (Supplementary Fig. S11, Fig. 5a). It must be pointed out that the physical characteristics of the coil (wire gage, diameter, number of turns, length, number of layers) given here are for the experimental results presented in this paper. These parameters as well as the duty cycle of the imposed voltage (which is 100 kHz for the results presented here) can all be easily changed depending on what effects one wishes to explore. It is important to ensure that the function generator (Hewlett Packard 33120A used in the present experiments) is able to drive sufficient current through the coil. In a similar manner, the holder can also be easily modified to accommodate a multi-well plate (Supplementary Fig. S6). Currents through the coil and the resulting magnetic inductions and induced electric fields can be calculated as described by equations (4) -(6) in the previous section for a 20 Vpp sawtooth voltage waveform at a duty cycle of 100 kHz (Supplementary Fig. S11, Figs. 5b-5d).

Analysis of actin filament distribution
Images obtained from phalloidin and fluorescence microscopy are imported into MATLAB (2014a, Mathworks, Inc., Massachusetts, U.S.A.). Individual cells are isolated and re-oriented so that their longest dimension is in the horizontal direction. Intensities are then separated into red, green, and blue so that the background and nuclei intensities may be filtered out and only the green fluorescence from the actin filaments is extracted. Actin fluorescence intensities are analyzed versus cell length (longer dimension being the length), and averaged. These postprocessed images and average intensities for the isolated cells shown in Fig. 6, are shown in Supplementary Figs. S12-S14.

Experimental results for "normal" breast epithelial cells (MCF-10A)
Experiments on combined chemotaxis and electrotaxis performed with MCF10A cells in the modified transmembrane assay utilized the growth factor EGF in the lower compartment of the modified transmembrane assay. After allowing 16 hours of incubation in the modified transmembrane assay, the cells that migrated to the other side of the Transwell membrane in the top chamber were stained with Hema 3 stain kit (Fisher Scientific, 122-911) according to the manufacturer's instructions. The stained cells were then photographed with a Zeiss microscope attached to a camera. The migrated cells were counted in 5 representative fields. As an illustration, representative fields are shown in Supplementary Fig. S15. Data for migration of MCF-10A cells with and without growth factor EGF and with and without induced electric fields, is shown in Supplementary Fig. S16. As can be seen from Supplementary Figs. S15-S16, MCF-10A cells hardly migrate without the presence of EGF (control in Supplementary  Fig. S16), and the presence of an electric field in the direction of migration ("North" side) has no statistically significant effect in this case in the absence of EGF (Coil North +E -EGF in Supplementary Fig. S16). On the other hand, it can be seen that EGF strongly promotes migration of MCF-10A cells (-E +EGF in Supplementary Fig. S16) and our induced electric field hinders their migration (Coil North +E +EGF in Supplementary Fig. S16) with statistical significance (p=0.002) for -E +EGF versus Coil North +E +EGF in Supplementary Fig. S16).
The glass wells are custom made to accommodate commercially available Transwell transmembrane inserts. The outer compartment and holder (Supplementary Fig. S2) are designed so that the membrane (the bottom surface of the inner funnel) is as close as possible to the outer surface of the coil, to within 1 mm.

Supplementary Figure S2
The holder is fabricated using 3-D printing technology after first developing a computeraided design (CAD) drawing using the software SolidWorks. The circular wells in the holder have unique dimensions based on the exact dimensions of each glass well (Supplementary Fig.  S1). The center channel allows the coil to be placed in the center so that there are 3 wells each on either side of the coil.

Supplementary Figure S4
Our modified transmembrane assay ( Fig. 1a and 1b) with the Transwell membrane inserts reproduces cell migration observed in the presently used multi-well plates with the same inserts. These cell migration experiments were performed over a period of 8 hours on SCP2 cells (N=3). No induced electric field was applied and the same media (0.1% FBS-DMEM) was used (p=0.993).
Photograph showing how the modified assembly for accommodating a culture plate ( Supplementary Fig. S7) may be altered for a 96 well multi-well plate. The holder is fabricated using 3-D printing technology after first developing a computer-aided design (CAD) drawing using the software SolidWorks.
Circuit diagram showing the use of a sense resistor to measure the current through the coil. The coil has a d.c. resistance, inductance, and intrinsic capacitance (Supplementary Fig. S8). Consequently, measurement of the current in the circuit by placing the sense resistance downstream of the coil, and measuring the voltage drop yields the total current flow (sum of conduction and displacement currents through the coil). This measurement at 1 kHz allows the intrinsic capacitance to be inferred by comparing the measured voltage trace across the sense resistance with a voltage trace predicted by a circuit element model that simulates the coil as a resistor in series with an inductor, both of which are in parallel with a capacitor (Supplementary  Fig. S8). This intrinsic coil capacitance is then used to calculate the conduction current at 100 kHz, relevant for the electrotaxis experiments reported here. It is important to mention that the current measurement described here is sensitive to stray capacitances that can arise from coax connectors (such as tees) placed at the oscilloscope. Therefore extreme care must be exercised to eliminate such sources of stray capacitance. Ultimately, a check of the measurement is the fact the current measured with the sense capacitance placed upstream of the coil should yield a similar current as when the sense capacitance is placed downstream of the coil.
Supplementary Figure S11 Predicted current through the electromagnetic coil used in the actin filament imaging experiments, at a duty cycle of 100 kHz for a 20 Vpp sawtooth voltage waveform. It can be seen that the derivative of the current through the coil is approximately symmetric over a single period of the duty cycle so that the electric field is in the leftward and rightward directions for different durations on the culture plate (when viewed from the top) ( Fig. 5b-5e).