Electrical and thermal characterization of ... - Springer Link

Biomed Microdevices (2006) 8: 25–34 DOI 10.1007/s10544-006-6379-5

Electrical and thermal characterization of nanochannels between a cell and a silicon based micro-pore Rubén E. D´ıaz-Rivera · Boris Rubinsky

C Springer Science + Business Media, Inc. 2006

Abstract Micro and nano fabrication techniques have facilitated the production of new devices for manipulation of single cells on a chip, such as the planar micro-pore electroporation technology. To characterize this technology we have studied the seal that forms at the interface between an individual cell and the micro-pore, in which the cell normally resides, as a function of an electrical field applied across the cell and temperature. Mathematical analysis of nonelectroporative electrical fields in experiments with MadinDarby canine kidney (MDCK) cells suggests that nanoscale channels form between the exterior of the cell and the pore wall. The results indicate that the electrical currents through these channels need to be considered when using planar micro-pores in general and performing micro-pore electroporation in particular. Our results show that the size of these channels is strongly temperature dependent and the cell to pore wall distance can increase by as much as 60% when the temperature of the system is lowered from 35 to 0◦ C. Temperature appears to be an important factor in the use of devices for cells on a chip and our results suggest that physiological temperatures should yield better seal formation, thus improved feedback sensitivity, than the traditional use of room temperature in planar micro-pore electroporation devices.

R. E. D´ıaz-Rivera () Department of Mechanical Engineering, University of California, Berkeley, Berkeley, CA 94720 Department of Mechanical Engineering, University of Puerto Rico at Mayagüez, Mayagüez, PR 00681 e-mail: [email protected] B. Rubinsky Department of Mechanical Engineering, University of California, Berkeley, Berkeley, CA 94720 e-mail: [email protected]

Keywords Micro-Electroporation · Biological cells · Micro-pore · Nanochannels

Introduction The cell membrane acts as a dynamic barrier between the interior and the exterior of the cell. The membrane has a high degree of transport selectivity, which preserves the microenvironment inside the cell. To study and intervene in the biochemical processes inside the cell, there is a need to bypass that selective barrier in a controlled manner. Several methods of a chemical, mechanical and electrical nature are used for this purpose. This work relates to the electrical method, which is widely known as electropermeabilization or electroporation. In electroporation, the permeability of the membrane can transiently increase when an appropriate external electric field pulse is applied across the cell. The induced permeabilization occurs due to the application of a high intensity electric field pulse (∼1 kV/cm) of short duration (∼10−6 to 10−1 sec) to cells or tissue (Weaver, 2003). During electroporation, it is believed that there is a rapid localized structural rearrangement within the membrane (Chang, 1992; Neumann et al., 1989; Tsong, 1991; Weaver, 2003). The lipid bilayer membrane rearranges to create water-filled pores, which provides a pathway for ions and molecules that normally are impermeable to the membrane. Electroporation of cells is traditionally performed in batches of cells suspended in a conductive media between two electrodes. Conventional electroporation is easy to implement and is commonly used to introduce a wide variety of chemical species into the cells. Nevertheless, the traditional process has some practical drawbacks that limit its performance. The electrical parameters that cause electroporation can vary between cells, and it is often difficult to Springer

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Biomed Microdevices (2006) 8: 25–34

achieve a high electroporation yield. Due to the uncontrolled nature of electroporation in suspended cells, it is common to find low cell survival rates and low transfection rates during the process (Golzio et al., 2001; Rols, 1994). In addition, the high voltage necessary to induce electropermeabilization of suspended cells can cause Joule heating of the solution, which leads to cell injury (Lee and Kolodney, 1987; Lee et al., 2000). In response to some of the technical problems associated with traditional electroporation and the inability of the technique to process cells in a controlled fashion, the field is moving towards the miniaturization of electroporation to target single cells. Single cell electroporation offers a variety of advantages over electroporation of suspended cells. These include: a) the use of extremely low voltages to induce electroporation, b) the capability to create concentrated high electric fields to induce site-specific electroporation c) means to manipulate as well as investigate the biochemical nature of single cells, and d) the ability to handle cell-to-cell variations in a population. In addition, electroporation theories can be better tested due to the singularity and sensitivity of these devices. Electroporation technologies employed to target single cells include carbon microelectrodes (Lundqvist et al., 1998), glass micropipettes (Haas et al., 2001; Rae and Levis, 2002) and electrolyte-filled capillaries (Nolkrantz et al., 2001). Another emerging single cell technology is based on the interaction between micro-pores (micro-apertures) on planar surfaces and cells. In planar micro-pore single cell electroporation technology, a cell is captured by pressure differential in a micro-pore on a flat substrate and the electroporation pulse is focused through the pore (Huang and Rubinsky, 1999). This technology and device employs electrical measurements across the cell for real time feedback and control of the electropermeabilization of individual cells (Huang and Rubinsky, 1999; Huang and Rubinsky, 2001; Huang and Rubinsky, 2003). The real time control is the key feature of this technology. In general, for optimal use of single cell manipulation technologies it is important to thoroughly characterize their micro and nano scale characteristics. This work focuses on the planar micro-pore structure system. The micro-pore technology is based on generating feedback and control from electrical measurements of currents and voltage across the cell and the pore. The quality and the nature of the seal can determine the sensitivity and the resolution of the feedback thus, understanding the electrical behavior of the seal is of great importance. This is not restricted only to the electroporation application of the planar-pore technology. For instance, in cell viability assessment by electrically probing the cell membrane, the seal quality will determine the difference in magnitude of electrical readouts between healthy cells and dead cells (Huang et al., 2003). In summary, understanding the electrical properties of the seal that forms Springer

between the cell membrane and wall of the micro-pore is important for the proper use of single cell technologies and is the general goal of this study. For planar micro-aperture type devices it has been shown that the single most important parameter that affects the resistance measurements of the seal is the cleft (distance between the cell membrane and the wall of the aperture) (Stett et al., 2003). Therefore, the particular goal of this study is to generate information on the electrical nature of the cleft between the cell membrane and the planar micro-pore. In this study the electrical characterization of the seal cleft was carried out as a function of temperature with Madin-Darby canine kidney (MDCK) cells. Temperature was considered in the range from 35◦ C to 0◦ C. Since it is well known that temperature affects both the electrical and mechanical properties of the cell membrane, perturbing the system with temperature could yield additional important information in the electrical characterization of the seal cleft. To study the seal cleft, a temperature controlled planar micro-pore type device was designed and fabricated with typical silicon microfabrication techniques. The experimental results were analyzed with a mathematical model of the electrical resistance in the cleft between the cell membrane and the planar device. The models were derived from the volume resistivity equation and the specific geometry defined by the cell trapped in the micro-pore. Different scenarios were considered depending on various assumptions of the mode in which cells deform when trapped in the micro-pore. The mathematical analysis of the electrical field in experiments with MDCK cells shows that nanoscale channels form between the exterior of the cell and the pore wall. The size of these channels was found to be strongly temperature dependent. The observed variations of the seal cleft distance as a function of temperature gives an improved understanding of the seal resistance in planar micro-pore configurations and suggest that there is an optimal operational temperature for the use of planar micro-pore single cell technologies.

Materials and methods Micro-pore fabrication The experiments were performed using a micro-pore structure fabricated on a dielectric substrate. Low stress silicon nitride (LSN) was chosen as the substrate material for the micro-pore fabrication because the microfabrication process involved is a well established technology and has been used to fabricate micro-electroporation devices in the past (Huang and Rubinsky, 1999). In addition, LSN is an optically translucent film, which is advantageous for performing transmitted light microscopy imaging.


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Fig. 2 System ensemble cross-section

Experimental set-up

Fig. 1 Cross-section of the fabrication process for the micro-pore in a low stress silicon nitride film

Figure 1 shows the step-by-step fabrication process for the micro-pore on the dielectric substrate. The process begins with a 100 n-type, double-side polished, single crystal Silicon (SCS) wafer. Low Pressure Chemical Vapor Deposition was used to deposit a 1 μm, low stress, silicon nitride layer on each side of the wafer (Figure 1a). Photoresist was spun on the top of the wafer and the micro-pore was patterned (Figure 1b). The patterned micro-pore was etched through the silicon nitride film using plasma etching. The diameter of the micro-pore was 3 μm. After stripping off the photoresist remaining on the top of the wafer, a new layer of photoresist was deposited and patterned on the backside of the wafer to open a window for the KOH etch step (Figure 1c). Then, the back window was opened with plasma etching (Figure 1d). Once the micro-pore and the back window were patterned on the silicon nitride layer, the wafers were dipped into a KOH solution (H2 O: KOH = 2:1 by weight) at 80◦ C to etch the exposed SCS all the way (Figure 1e). Finally, a 0.1 μm silicon dioxide isolation layer was thermally grown over the exposed SCS after the KOH etch (not shown).

In order to use the micro-pore structure effectively, it was placed between two chambers (see Figure 2). The top chamber served as a place to put the cells in suspension in a solution of physiological saline (detailed later). The bottom chamber was used to create the negative pressure needed to trap the cells in the micro-aperture. Both chambers were created by bonding two annular Ag/AgCl electrodes (In Vivo Metric Biomedical Products, E203-R, Healdsburg, CA) to the substrate. The electrodes were mounted on epoxy housing with low water absorption and a low dielectric constant (Henkel Loctite Corp., Hysol 6C, Avon, OH). Finally, the bottom chamber was sealed by bonding the bottom electrode with an acrylic substrate. The acrylic substrate contained inlet and outlet fluid ports that were used to control the pressure in the system. The temperature was controlled by mounting the system ensemble onto a thermally conductive substrate attached to a thermoelectric cooler (Melcor Corp., SH 1.0-125-06, Trenton, NJ). The micro-electroporation chip ensemble embedded in the thermal substrate is illustrated in Figure 3. Since the thermoelectric cooler (TEC) only moves the heat from one side to the other, there is a need to dissipate the heat from the hot junction. To remove the heat from the TEC, a water-cooled heat exchanger with a hole in the middle was fabricated. The heat exchanger consists of a disk shaped aluminum piece with an annular cavity inside. The water flows from one side of the heat exchanger to the other, removing the heat from the Peltier effect device. Silver-based thermal compound (Arctic Silver III, Visalia, CA) was used to minimize contact resistance among thermally conductive surfaces. The TEC was controlled with a PID fuzzy logic temperature controller (Fuji Electric Corp., PXV3, Saddle Springer

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Fig. 3 Side view of the system ensemble coupled with the temperature controlled stage (not to scale)

Brook, NJ). The TEC was connected to a DC power supply through a solid-state relay. The solid-state relay was turned on or off by the PID temperature controller depending on the set point and the temperature feedback. The temperature was measured with a T-type thermocouple (Therm-x of California, Union City, CA). The electronics and software were provided by Excellin Life Sciences (Menlo Park, CA). The details of the electronics have been described elsewhere (Huang et al., 2003). To transmit data from the electronics box to the computer, a National Instruments Data Acquisition Card was used (DAQCard-6062E, Austin, TX).

Fig. 4 Typical system calibration measurement showing the applied voltage, the measured current and the calculated resistance (system without a cell embedded in the micro-pore). Notice the resistance is around 150 k. Each calibration measurement was performed before and after the experimentation pulse. This procedure was done to ensure that the pore was clear from any biological debris.

Cell preparation The electrical recordings were performed on Madin-Darby canine kidney epithelial cells (UCSF Cell Culture Facility, San Francisco, CA). The cells were grown in an incubator supplied with 5% CO2 at 37◦ C. The cultivation was done using Dulbecco’s Minimum Essential Medium (Invitrogen Corp., Carlsbad, CA), Earle’s balanced salt solution supplemented with 10% fetal bovine serum, 1% non-essential amino acids, 1% penicillin, and 2 mM of L-glutamine. For electrical characterization experiments, the culture medium was replaced by Dulbecco’s phosphate buffered saline (136 mM NaCl, 8 mM Na2 HPO4 , 2.7 mM KCl, 1.5 mM KH2 PO4 , Invitrogen Corp., Carlsbad, CA). The cells where removed from the culture flask by using 0.25% Trypsin/EDTA (Invitrogen Corp., Carlsbad, CA). Two phosphate buffered saline (PBS) washes were performed prior to the addition of Trypsin/EDTA. Experimental procedure In a typical experiment, both chambers were filled with PBS and cells were introduced into the top chamber via a micropipette. Before and after each experiment, a system calibration measurement was performed by the application of an electrical squared pulse (see Figure 4). This procedure was done to ensure that the pore was clear from any biologiSpringer

cal debris. A negative pressure difference of −2.0 ± 0.1 kPa was applied across the pore to trap a cell in the pore. The applied pressure was carefully monitored with a digital readout of a solid-state low-pressure sensor (GE Novasensor, NPC-1210015D-3S, Fremont, CA) and maintained constant throughout the experiments. The low pressure zone around the micro-pore pulled the closest cell into it in a matter of seconds, and the cell effectively clogged the micro-pore. Once the cell was trapped in the micro-pore, the system was on hold for one minute to achieve seal and temperature stabilization. Immediately after that, the temperature was ramped from 35 to 0◦ C in 8 minutes. Recordings of DC currents across the pore with the cell were performed at a frequency of 30 seconds, producing data points at specific temperatures. For each data point, one 150 mV squared pulse was applied for 100 ms to the system with a trapped cell while the current was measured. Since the purpose of this study is to characterize the seal between the cell and the pore surface, the amplitude of the applied voltage pulse was below the critical threshold needed to induce electropermeabilization in cells at all times. The seal resistance was calculated us ing Ohm’s law where Rseal = V I . Figure 5 illustrates a typical resistance plot for a cell trapped in the micro-pore when excited with a low voltage square pulse. Notice that the resistance is constant over the time the system was excited which means that the system is at steady state.


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Fig. 5 Typical resistance calculation from electrical measurements for a cell embedded in the micro-pore at 35◦ C

Theoretical estimation of the seal cleft Studies on single cell deformation due to micropipette aspiration have been reported earlier (Discher et al., 1998; Drury and Dembo, 1999; Hochmuth, 2000). The deformation of a cell trapped in a planar micro-pore is very similar to that which occurs during micropipette aspiration. The shape of the deformed cell in a planar micro-pore structure has been observed by others (Sugár et al., 2003), and the observation is consistent with ours. The observed deformation is depicted in a graphic representation in Figure 6. The representation is a vertical cross section through the pore and the cell and is not to scale. When the cell is trapped in the micro-pore, the cell membrane deforms in such a way as to fill the cylindrical cavity of the pore. The figure shows that the cell membrane is not in contact with the walls of the micro-pore. This is a standard assumption based on the fact that there is measurable current flow across the pore. Intimate contact would produce a perfect seal and no current, which does not happen in planar pore-cell configurations. The existence of current flow at low, sub-electroporation potentials across the pore and cell implies that there must be an annular sheath of conductive media between the cell membrane and the wall of the micro-pore. The space occupied by this sheath of conductive media is referred to in this work as the seal cleft. For the purposes of this study, the parameter utilized to evaluate the electrical phenomena between the cell and the aperture wall is the seal cleft distance. In order to estimate the seal cleft distance, a mathematical formula for the system’s resistance was developed. The seal cleft distance was then estimated from the correlation of the experimental measurements to the theoretical model of the system. To develop the mathematical formulations, the areas of proximity between the cell membrane and the silicon surface had to be identified. The primary area of proximity was identified as the wall of the micro-pore where the seal formation is believed to form the seal cleft distance. The secondary area

Fig. 6 Visual representation of the areas and variables included in the resistance calculation for Model I where δ is the seal cleft distance, ι is the thickness of the LSN film, rpore is the radius of the micro-pore, and rcell is the cell radius. The area with horizontal stripes represents the primary proximity area. The area with vertical stripes represents the secondary proximity area. y(θ) and x(θ ) are the height and the radius for each annular section in the secondary proximity area as a function of θ, where θ is the angle between the horizontal center line and the radial distance of the cell membrane at the point of interest. The drawing is not to scale.

of proximity was identified as the planar surface surrounding the micro-pore. For our calculations, it was assumed that the primary proximity area was always active. However, since we could only see a top view image of the cell trapped in the micro-pore, the extent to which the cell membrane was in contact with the surface in the secondary area was not known. Therefore, two models were developed to consider different possibilities for the secondary proximity area. Model I considered the resistance created by the seal cleft and the resistance created by the space between the cell envelope and the planar surface surrounding the micro-pore (see Figure 6). For Model I, the cell envelope outside the micropore was assumed to retain a spherical shape. This assumption would define the geometry of the secondary proximity area. The mathematical expression for Model I is derived from the well-known volume resistivity equation, R=

ρL A

(1)

where R is the resistance, ρ is the volume resistivity, L is the length of the control volume and A is the cross sectional area of the volume. This equation can be easily adapted to estimate the resistance contribution for the two areas under Springer

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consideration for Model I. The primary area was modeled as an annular section with thickness δ and length ι + δ, where δ is the seal cleft distance and ι is the thickness of the LSN film. The secondary area was modeled as an integration of a series of annular sections positioned between the extracellular surface of the cell membrane and the nitride surface (see Figure 6). The height and the radius for each annular section are given by y(θ ) and x(θ) respectively, where θ is the angle between the horizontal center line and the radial distance of the cell membrane at the point of interest. These two dimensions depend on θ since, for Model I, the geometry of cell membrane outside the micro-pore was considered of spherical shape. Once the integration was carried out for the secondary proximity area, the mathematical formula for Model I can be expressed as follows: RModel I = Rprimary + Rsecondary Rprimary =

ρpbs (ι + δ) π (2δrpore − δ 2 )

Rsecondary = ⎛ ⎞cos−1(rpore /rcell ) ln[cos[θ 2] − sin[θ 2]] +⎟ ⎜− δ ⎜ ⎟ ⎟ ρpbs a ⎜ ⎜ ln[cos[θ 2] + sin[θ 2]] + ⎟ ⎜ ⎟ 2π rcell ⎜ δ + 2rcell ⎟ ⎝ r ln [δ + r − r sin [θ]] ⎠ cell cell cell δ (δ + 2rcell ) 0 where ρpbs is the temperature dependant volume resistivity of phosphate buffered saline, rpore is the radius of the micropore, rcell is the cell radius and a is the difference between the cell and pore radius. For Model II, it was considered the possibility of the cell membrane to become deformed outside the pore due to the applied pressure differential. This is shown in Figure 7(A), were the primary proximity area is represented with horizontal stripes and the secondary proximity area is represented with vertical stripes. In Model II, the distance between the cell membrane and the nitride surface in the primary and the secondary proximity area were considered to be the same (δ). Therefore, the seal cleft is going to have a stronger dependence on the secondary proximity area in Model II when compared to Model I. The mathematical description of Model II can be written as follows: RModel II = Rprimary + Rsecondary ρpbs (ι + δ) Rprimary = π (2δrpore − δ 2 ) ρpbs Rsecondary = [ln(1 − n[1 − rcell /rpore ])] 2π δ As it was mentioned before, the extent to which the cell envelope outside the micro-pore was deformed could not be Springer

Fig. 7 Visual representation of the areas and variables included in the resistance calculation for Model II where h is the extent of the cell membrane that is outside the pore and has proximity of δ with respect to the planar nitride surface. (A) Illustrates the cell trapped in the micro-pore while the cell envelope is deformed. The drawing is shown with two axes of symmetry to point out the details. (B) Shows the cell envelope deformation and the active area for resistance calculation for low surface tension. (C) Illustrates the cell envelope deformation and the active (shaded) area for resistance calculation for high surface tension

determined from microscopic observations. Therefore, several scenarios were considered for Model II, bounded by two limiting conditions. The limiting conditions were taken from results found in the literature, where biological cells are modeled as slippery droplets of Newtonian fluid (Drury and Dembo, 1999). The limiting conditions are low and high surface tension of the cell membrane as shown in Figure 7(B) and Figure 7(C) respectively, where h is the extent of the cell membrane that is outside the pore and has proximity of δ with respect to the planar nitride surface. Low surface tension implies that h is equal to the cell radius minus the pore radius and is represented in our model by setting n equal to one (see Figure 7(B)). On the other hand, high surface tension implies that the cell envelope does not deform (retains spherical shape), and is represented in our model by setting n to zero (see Figure 7(C)). In addition to the limiting cases, h was also considered to fall between rcell and rpore . This was done by setting n equal to 0.75, 0.5 and 0.25. Notice that the high surface tension scenario in Model II is similar to


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the scenario presented in Model I. The difference is that in Model II (n = 0) the seal cleft proximity area was the only one considered while in Model I the area under the spherical cell envelope as well as the area in the seal cleft were considered. Both models employ similar variables and constants. The constant values used throughout the computation for the seal cleft estimation are as follows, rcell = 10 μm rpore = 1.5 μm ρ@20◦ C = 1 1.3 · m α = 3.16742 × 10−2 ◦ C−1 ρ@20◦ C ρpbs (T ) = 1 + α (T − 20◦ C) where ρ@20◦ C is the resistivity of PBS at 20◦ C, α is the electrical resistivity coefficient and ρpbs (T ) is the mathematical representation of the temperature dependent electrical resistivity of ionic medium. The values for the electrical resistivity of PBS were experimentally measured as a function of temperature with a standard electrical conductivity meter (Cole Palmer, AcornTM CON 5 meter, Vernon Hills, IL). These values were consistent with experimental values published elsewhere (Grimnes and Martinsen, 2000). Finally, α was computed by curve fitting the electrical resistivity of PBS found experimentally with the mathematical expression of ρpbs (T ).

Results System calibration measurements were performed before the electrical probing of single cells in the micro-pore. The resistance of the system as a function of temperature is shown in Figure 8. The diamond marker curve is the resistance calculated from electrical recordings performed on the system with phosphate buffered solution in both chambers and no cell. The circular marker curve is the resistance estimation of the system without cells, calculated by evaluating Eq. (1) for a cylindrical channel with the dimensions of the micropore. The numerical values for the diameter and length of the channel used in the volume resistivity equation were 3 μm and 1 μm respectively. It is important to mention that for the system resistance estimation, the resistance contribution from the top and bottom chambers was considered negligible. This assumption comes from the fact that the electrical resistance of the chambers is about three orders of magnitude smaller than the resistance of the micro-pore. As expected, the trend of the resistance obtained from the volume resistivity is the same as the one obtained by electrical measurements of the system. However, there

Fig. 8 System calibration measurements. The series with the diamond marker represents the resistance calculation from the experimental data for the system calibration. The series with the circular marker is the theoretical resistance computed using the volume resistivity equation for a pore diameter of 3 μm

is an offset between the curves. This is attributed to the electrode/electrolyte interface impedance. Nevertheless, the magnitude of this offset (∼80 k) is negligible in comparison to the magnitude of the experimental resistance with cells embedded in the micro-pore (∼3 to 8 M, see Figure 9). With the current experimental system set up, seals between biological cells and the wall of the micro-pore that gave resistance measurements on the order of M’s were easily achieved. The order of magnitude of these measurements is consistent with measurements made by others with planar micro-pore systems (Huang et al., 2003; Stett et al., 2003). Figure 9 shows resistance measurements across cells trapped in the micro-pore. It is important to restate that the electrical potential applied to make these measurements is well below the electropermeabilization threshold of cells in our system.

Fig. 9 Average resistance measurements for cells trapped in the micropore under non-electroporative conditions. Ten MDCK cells were electrically probed at each temperature. The error bars stand for one standard deviation (± 1σ ). Notice the experimental resistance increases with lowering temperature. This effect is mainly due to the electrical properties of PBS

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Each data point represents the average resistance for 10 different cells at the specified temperature. All measurements add up to 170 electrical recordings. Notice in Figure 9 the increase in resistance with a decrease in temperature. This may be expected from the existence of the seal cleft. Therefore, what is being measured is the bulk electrical resistance of the PBS found between the cell membrane and the nitride surface. However, the trend from the curve in Figure 9 is not consistent with the one found in the calibration experiments as depicted in Figure 8. This inconsistency implies that there are other variables involved besides the temperature dependence on the resistivity of PBS. From examination of the volume resistivity equation, this deviation appears to be geometrical in nature, related to the dimensions of the seal cleft. In order to get a smoother curve for the seal cleft as a function of temperature, the data on Figure 9 was curve-fitted with a five-order degree polynomial. Once the experimental resistance values were plugged into the equations for Model I & II, the dimensions of the seal cleft were estimated. These results are shown in Figure 10 and 11 for models I and II respectively. Model I shows a constant increase in the seal cleft when the temperature is lowered from 35 to 0◦ C. The distance appears to increase from about 22 nm to 34 nm, which is considerable. In addition, it can be observed that the calculated cleft size goes to a minimum when the temperature approaches physiological conditions. Model II shows the same behavior as Model I, however the magnitude of the calculated cleft size may vary significantly with the model considered. For the case that the entire radius of the cell envelope is considered to be in close proximity with the nitride surface (n = 1), the minimum cleft distance is around 70 nm whereas in the opposite case (n = 0), the minimum is close to 19 nm. This large difference tells us that the secondary area of proximity may play an important role on the seal formation on planar substrates. This is mainly because planar substrates provide a greater proximity area than a traditional

Fig. 10 Calculated seal cleft values as a function of temperature for Model I

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Fig. 11 Calculated seal cleft values as a function of temperature for Model II

micropipette, and could improve the chances of achieving a high resistance seal. If we examine Figure 10 and 11 in more detail, it can be observed that the seal cleft curve from Model I falls in between the curves of n = 0 and n = 0.25 from Model II. Nevertheless, from this information we cannot determine which model is more appropriate. In order to compare the two models more effectively, the seal cleft curves were normalized with respect to the minimum distance (δ@32 ◦ C ). The normalization would allow us to compare the two models on the same dimensionless scale (see Figure 12). It is clear from Figure 12 that even though the results using the two models produce a similar trend, the actual increment in the cleft dimension with temperature differs between the models. However, the difference is not great since they differ by no more than 10%. The similarity in the results between the models shows that even though the extent of the proximity area has a strong influence in the magnitude of δ, the temperature dependence is virtually the same for both models. Therefore, the strong temperature dependence of the seal cleft size estimated by our models illustrates the relevance of temperature on the seal formation.

Fig. 12 Normalized seal cleft curves for Models I & II. The curves were normalized with respect to the minimum δ(δ@32◦ C)


Discussion Figures 10, 11 and 12 show the mathematical estimation of the seal cleft as a function of temperature. The overall trend for δ in both models is to increase as the temperature decreases; however, the numerical values vary significantly with the model used. At room temperature (T=20◦ C), the estimated values for the seal cleft ranges form 20 to 80 nm, depending on the model or case within a model. The estimated values for δ reported in this manuscript are on the same order of magnitude as the ones reported elsewhere in systems similar to ours or where cells were adhered to a tailored substrate (Braun and Fromherz, 1998; Stett et al., 2003). However, the nature of membrane-surface distances that are in the nanometer range and are encountered in micro-pore systems is not known. The formation of the nanochannel between the cell membrane and the wall of the pore could be due to several factors, like the membrane affinity to the substrate material, the roughness of the substrate material and the presence of extracellular membrane constituents. It is well known that biological cells adhere preferentially to certain materials like glass. Glass is the material of choice to perform electrophysiology experiments (patchclamp) where the seal resistance is in the order of magnitude of one G. The sensitivity of the system needed to perform single ion channel recordings is largely dependent on the seal cleft distance. It has been estimated that the membrane-glass distance needed to perform electrophysiology experiments is in the order of magnitude of tens of Angstroms (Corey and Stevens, 1983). Membrane-LSN surface distances are nowhere near tens of Angstroms as estimated by our calculations. Therefore, the preferential membrane affinity to substrate materials could play a major role in the formation of nanochannels between the cell membrane and the wall of the pore in our system. The adhesion between a biological surface and a solid substrate is not well understood. Based on experimental data, the adhesion has been attributed to molecular interactions, van der Waals interactions and capillary forces mediated by a wetting solution between surfaces (Arzt et al., 2003). All the interactions mentioned above are dependent on the surface properties of both the biological and substrate materials. Hence, the roughness of the substrate material and the presence of extracellular membrane constituents could be of importance as well. The most common method for characterizing surface roughness is Ra (the arithmetic average of the absolute deviation from the mean surface level). The surface roughness has been calculated and reported elsewhere as 2.9 nm for 1 μm LPCVD low stress nitride depositions (Ra value calculated from a 20 × 20 μm2 atomic force microscope (AFM) scan, (Sanchez et al., 1997)). This means that, in average, there

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are protrusions on the surface of the nitride with height of 2.9 nm. The surface roughness alone cannot account for the estimated values of δ reported here (e.g. form 20 to 80 nm at 20◦ C). However, it is known that surface roughness reduces the adhesion between surfaces by lowering the real contact area, which may decrease the proximity between surfaces (Persson et al., 2005). The presence of biological constituents on the extracellular side of the cell membrane can increase or decrease the membrane-LSN surface distance. This is due to the properties of the various components found on the membrane outer surface. For example, some of the cell proteins found at the surface of cells can bind to other cells or to extracellular matrices. The proteins that promote membrane adhesion to biological material and substrates are called cell adhesion molecules. These molecules are likely to decrease the magnitude of δ by establishing either a focal or a broad contact with the substrate surface (Giebel et al., 1999). On the other hand, there is also a carbohydrate coating on the outer surface of the cell membrane, which one of the likely functions is to protect cells against mechanical and chemical damage and to keep foreign objects at a distance (Alberts, 2002). This carbohydrate coating is known as the glycocalyx and it is present in all eukaryotic cells. It is known that the extracellular surface of the apical membrane of most epithelial cells has a glycocalyx thickness in the order of magnitude of tens of nanometers (Rosenberg, 1995). Therefore, the cell coating can be visualized as a mechanical stop between the extracellular surface of the cell membrane and the walls of the nitride pore thus forming the nanoscale passage. Even though the factors discussed above can justify the existence of the nanochannel between the cell membrane and the pore wall, they cannot explain the temperature dependence of δ as estimated by our calculations. Especially when the seal cleft distance is strongly temperature dependant (as estimated by our models, see Figure 12). Then, why does the membrane-surface distance increase with decreasing temperature? This behavior can be explained in terms of the cell membrane fluidity. When the cell is trapped in the micro-pore, a drastic deformation of the cell envelope takes place (Sugár et al., 2003). In our experiments, the applied pressure was constantly monitored. This was done to achieve a constant pressure gradient throughout the experimental procedure, thus eliminating one possible perturbation variable. However, the fluidity of the cell membrane has strong temperature dependence. The fluidity of the cell membrane is quantified by the membrane microviscosity. It has been shown in the literature that the microviscosity of lipid bilayers increases quite significantly with decreasing temperature (Dimova et al., 2000; Wang and Hu, 2002). In fact, the trend of the microviscosity of the cell envelope with temperature is remarkably similar to Springer

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the seal cleft dimension trend. In terms of the biophysical behavior, the membrane surface tension becomes stronger as the system is cooled, which means the membrane has a greater ability to oppose a deformation of the cell membrane. This could potentially translate to an increase in the membrane-surface distance, since the applied pressure is constant. It is clear from Figure 12 that the seal cleft distance increases as much as 50 to 60 percent when the temperature is lowered from 35 to 5◦ C. This change is not as drastic when the temperature is lowered to 20◦ C from physiological conditions, where the increment is about 15 percent. Nevertheless, considering that most electroporation protocols are performed at room temperature, it can be argued that the membrane-LSN distance that forms close to physiological temperatures could improve the chances of getting a better seal thus increasing the sensitivity of the system. This is especially important in planar micro-pore electroporation systems where current feedback is of great importance and real time controlled single cell electropermeabilization is desired.

Conclusion Advances in nano and micro fabrication techniques have led to the development of new devices for the manipulation of individual cells on a chip. One example of these devices is the planar micro-pore electroporation chip. In these devices, electrical fields are imposed across an individual cell, which normally resides in a micro-pore within the device. The interface between the cell and the pore wall plays an important role in the performance of the device. Typical silicon microfabrication techniques have been used to create a system that can probe the cleft between the cell and a micro-pore wall as a function of an electrical field applied across the cell and as a function of temperature. A mathematical analysis of the non-electroporative electrical field, which develops in the cleft between the cell membrane and the micro-pore walls, shows that channels of nanoscale size form. These channels are strongly temperature dependent and can increase about 60% in size from physiological temperatures to 0◦ C. The temperature dependence of the cleft size may be related to the fluidity of the cell membrane, whose temperature dependence exhibits a similar pattern. It appears that temperature is an important factor in the use of devices for cells on a chip. Our results suggest that performing in vitro experimentation at or close to physiological temperatures should yield higher quality seals and better sensitivity than the traditional use of room temperature in planar microelectroporation systems. This argument is based on the fact that a smaller cleft distance, which means a better seal, translates to an increase in sensitivity for real time current feedSpringer

back in single cell electroporation with planar micro-pore systems.

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