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Copyright © 2005 The Biophysical Society. All rights reserved.
Biophysical Journal, Volume 89, Issue 5, 3628-3638, 1 November 2005

doi:10.1529/biophysj.104.049809

Electrophysiology

Cell-Transistor Coupling: Investigation of Potassium Currents Recorded with p- and n-Channel FETs

Günter Wrobel^*, 1, Reinhard Seifert^†, 1, Sven Ingebrandt^*, Jörg Enderlein^†, Holger Ecken^*, Arnd Baumann^†, U. Benjamin Kaupp^† and Andreas Offenhäusser^*, ,  

^* Institute of Thin Films and Interfaces (ISG2) and Center of Nanoelectronic Systems for Information Technology, and
^† Institute of Biological Information Processing (IBI1), Research Centre Jülich, D-52425 Jülich, Germany

Address reprint requests to Andreas Offenhäusser.

¹ G. Wrobel and R. Seifert contributed equally to this work.

The extracellular recording of cellular activity provides a powerful, noninvasive technique that holds great promise for biomedical studies. In contrast to classical electrophysiological methods, silicon devices allow stable long-term recordings of electrical activity from single cells or networks of cells cultured on planar surfaces. Signals from neurons or other electrically active cells have been recorded using microelectrode arrays of metallized electrodes on glass or silicon substrates 1 or nonmetallized field-effect transistors (FET) 2,3. Such devices have also been used to stimulate neurons electrically 4,5,6.

The “open gate” of a FET can register the electrical activity of cells attached to the gate region 2,7. Changes in the drain-source current of the FET are correlated with voltage changes in the small cleft between cell and transistor surface 8,9. The extracellular voltage signals have been interpreted in terms of equivalent electrical-circuit models. For example, the point-contact model describes the electrical coupling between a cell and a transistor gate by a single point of contact 10. The model has been further developed to incorporate a two-dimensional contact area 11. Subsequently, properties of the cell membrane have been incorporated, such as the specific membrane conductance and the surface area of the membrane-transistor contact 9,12. Despite these improvements, the models do not adequately describe several aspects of the extracellular signals. For example, the amplitude and the time course of the FET signals produced by A-type and K-type potassium currents in hippocampal neurons are not adequately predicted 13. The initial current transient that is mediated by rapidly inactivating A-type K⁺ channels was missing in the transistor signal. Moreover, the transistor signals that were recorded during activation of K-type K⁺ channels were significantly larger than predicted by the simulation. To account for these discrepancies, it has been proposed that K-type K⁺ channels are enriched, whereas A-type K⁺ channels are depleted from the contact area 13,14. Accumulation of channels has also been proposed for maxi K⁺ channels expressed in HEK 293 cells 14.

To advance our understanding of the nature of the FET signals, we coupled HEK 293 cells that expressed a voltage-gated K⁺ channel to n- and p-channel FETs. The ion channel belongs to the family of ether-á-gogo (EAG) channels. The kinetics of EAG channel activation strongly depends on the voltage-step protocol and the presence of extracellular divalent cations, for example Mg²⁺ and Co²⁺15,16,17,18. Thereby, this cell system provides a unique opportunity to modulate the kinetics and shape of whole-cell membrane currents and to compare it with the recorded FET signals.

We find that, for fast EAG channel activation, the increase of the FET signal is slower than the time course of the whole-cell current. Moreover, when the whole-cell current rapidly turned off by repolarization, the FET signal declines with two kinetic components: a fast component that follows the whole-cell current and a slow component that seems to be unrelated to the whole-cell current. The slow component differs strongly in amplitude between p- and n-channel FETs and cannot be explained by the redistribution of ion channels.

The p-channel FET devices used for the extracellular recordings were first described by Offenhäusser et al. 19. Here we used an improved version: a second implantation step for drain-source doping reduced the series resistance of the contact lanes and, thereby, decreased the noise level of the p-channel transistor 20. In addition, we used n-channel transistors with a lower noise level that were fabricated according to Krause 20. A shallow implant through a 220-nm SiO₂ layer in the gate area buried the n-channel; this procedure lowered the 1/f noise 21.

Both types of FETs consisted of 16 transistor gates arranged in a 4×4 matrix (100 or 200μm pitch) in the center of a 5×5mm² silicon chip. Gate oxide was fabricated by thermal oxidation of silicon (8-, 10-, or 12-nm thickness). The gate oxide area exposed to the electrolyte solution was 5×8μm², 6×8μm², or 7×8μm². Effective gate length of the FETs was 1–2μm. The transconductances were g_m=0.2–0.6mS for the p-channel and 0.5–1.4mS for the n-channel devices, depending on the thickness of the gate oxide and the gate dimensions. The root mean-square noise was ∼100μV for p-channel and ∼45μV for n-channel transistors. The surface of the chips was passivated by an ONO layer (SiO₂ / Si₃N₄ / SiO₂), which allowed multiple reuses of the chip. Details of the fabrication, the encapsulation process, and the amplifier systems have been described elsewhere 19,22,23.

The FET setup used in this study has been previously described 22. In the working point, a constant working current of the FET of 0.1–1mA (depending on the FET design) superimposed the recorded changes of drain-source current I_DS. The FET amplifier system used a feedback circuitry, which subtracted the output signal from the baseline and compensated the constant dc-offset 24.

The working point of the FETs was determined by measuring the transfer characteristics I_DS (V_GS). The p-channel FETs were biased with drain-source voltages V_DS and gate-source voltages V_GS from 0 to −3V, and the n-channel FETs with voltages from 0 to +3V. An extracellular Ag/AgCl electrode, which was set to ground potential, served as reference electrode for both the gate contact of the FETs and the patch-clamp recordings. Thus, the source and the bulk of the FETs had to be set to a positive voltage to result in negative V_GS for the p-channel FETs and to a negative voltage to result in positive V_GS for the n-channel FETs.

The K⁺ ion sensitivity of the FETs (S_FET) has been studied with solutions of from 0.1mM to 1M KCl (10mM HEPES, pH 7.4, adjusted with TRIS) with constant ionic strength of 2M (adjusted with CaCl₂). We found a nonlinear relationship for the response of p-channel FETs: 0.7±0.5mV/pK for K⁺ concentrations and 3.8±1.7mV/pK for These values were smaller compared to those reported in literature: 6–8mV/pK (for ) up to 10–15mV/pK (for ) 25.

The chip surface was cleaned twice by ultrasonification for 5min in 2% (v/v) Hellmanex II (Hellma, Müllheim, Germany) and bidistilled water. The surface was further treated by incubation in 20% (v/v) H₂SO₄ for 20min at 80°C. The chips were rinsed with bi-distilled water and kept for 5min in 99.8% (v/v) ethanol. After rinsing two times with PBS buffer (137mM NaCl, 2.7mM KCl, 8.1mM Na₂HPO₄, 1.5mM KH₂PO₄, pH 7.3), FET surfaces were coated for 30min with 25μl of 0.1mg/ml poly(l)lysine (Sigma, Taufkirchen, Germany) at room temperature. The surfaces were rinsed with PBS before plating the cells.

The beag1 gene 16 was subcloned from a pcDNA1.1 construct into the BamHI and XbaI restriction sites of a pcDNA3.1 vector (Invitrogen, Breda, The Netherlands) by standard cloning techniques. Approximately 10μg of the recombinant plasmid DNA were introduced into exponentially growing HEK 293 cells (∼2×10⁵ cells per 50-mm dish) by a modified calcium phosphate method 26. Cells were grown in minimal essential medium (M2279, Sigma) supplemented with 2mM glutamine, nonessential amino acids, 10% (v/v) fetal calf serum, 100units/ml penicillin, and 0.1mg/ml streptomycin (M10 medium). Transformed clones were selected in the presence of 1.0mg/ml of the antibiotic G418 (Sigma). Isolated foci were propagated in M10 medium with 0.8mg/ml G418. Expression of EAG channels was determined by electrophysiological recordings.

Cells were cultured in 50-mm dishes and split weekly. For plating onto the FET chips, the cells were trypsinized for 5min at 37°C (0.5mg/ml trypsin; 0.2mg/ml EDTA, Sigma). Detached cells were suspended in M10 medium and centrifuged for 5min at 200×g. Cells were plated onto the poly(l)lysine-coated FETs at densities of 4500–6000 cells per chip (effective chip surface, 6.2mm²). The chips were kept at 37°C and 5% CO₂ for 3–5 days in a humidified chamber. Fig. 1 shows a microscope image of HEK 293 cells grown for 4 days on a gate structure.

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Figure 1

Differential interference contrast micrograph of HEK 293 cells on a poly(l)lysine-coated chip surface after 4 days in culture (left) and a schematic drawing of the FET (right). The gate of the transistor (width, 8μm; length, 5μm) inside the gate window is connected to the drain (top) and the common source (bottom). Scale bar=20μm.

After 3–5 days in culture, membrane currents were recorded by the patch-clamp technique in the whole-cell configuration 27 with an EPC-9 patch-clamp amplifier (HEKA Elektronik, Lambrecht, Germany). Changes of I_DS of the transistor located below the patch-clamped cell were amplified and fed into the external input of the EPC-9 patch-clamp amplifier.

Membrane current signals and corresponding FET signals were recorded simultaneously at 12kHz and averaged using the TIDA software (HEKA Elektronik). Patch pipettes (3.8–5.2 MΩ) were filled with intracellular solution (125mM KCl, 2mM MgCl₂, 10mM EGTA-KOH, 10mM HEPES, 5mM Na-ATP, adjusted to pH 7.4 with KOH). The extracellular solution was 5mM KCl, 140mM NaCl, 10mM HEPES, 5mM glucose, adjusted to pH 7.4 with NaOH. By adding different divalent cations we obtained extracellular Ca²⁺ solution (1mM CaCl₂), extracellular Ca²⁺/Mg²⁺ solution (5mM MgCl₂, 1mM CaCl₂), and extracellular Ca²⁺/Co²⁺ solution (2mM CoCl₂, 1mM CaCl₂). In the following, these solutions will be referred to as Ca²⁺-, Mg²⁺-, and Co²⁺ solutions. The presence of Ca²⁺ in all solutions was required for sufficient patch stability. The membrane capacitance of the cells (n=52) was C_M=15.4±4.0pF, the membrane resistance was R_M=2.8±1.7 GΩ, and the series resistance of the cell-pipette contact was R_S=10.9±4.9 MΩ. The values of C_M and R_S were compensated by the EPC-9 amplifier using the TIDA software 28,29.

Recordings from cells that only partially covered the transistor gate showed smaller amplitudes, leading to a significantly lower signal/noise (S/N) ratio. Therefore, we describe only signals recorded from cells completely covering the FET gates.

We chose a cell line expressing EAG channels to study the nature of the contact at the cell-transistor interface. The activation kinetics of the channel can be manipulated by various means. Therefore, this channel is suitable to test, whether the changes in the gate voltage of the FET (V_FET) faithfully recapitulate the changes in membrane current (I_M). A fraction of I_M flows through the cleft between the attached cell membrane and the surface of the transistor gate. This current causes a change in the gate voltage 8,9.

The activation kinetics of EAG channels, and thus the time course of I_M can be modulated by two different maneuvers 15,16,17,18: by variation of the pulse protocol (hyperpolarizing prepulses), and by addition of divalent cations (Mg²⁺ or Co²⁺) to the extracellular solution. The EAG channel adopts slow and fast gating modes depending on the holding voltage from which the channel becomes activated. When activated from a more negative voltage compared to the holding voltage, the channel opens with a characteristic sigmoidal time course. This decelerated activation is particularly pronounced in the presence of extracellular Mg²⁺ and Co²⁺ ions, which promote the transition from the fast to the slow activation mode of the channel.

We applied rectangular depolarizing pulses to EAG-expressing HEK 293 cells that covered the gate of a FET (Fig. 1) and recorded simultaneously I_M in the whole-cell configuration with a patch pipette and V_FET with a FET device. The time course of I_M displayed the same characteristics as previously described for voltage-gated EAG currents 15,16,17 (Figure 2AC).

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Figure 2

Comparison of the time course of whole-cell membrane currents (I_M) and p-channel FET signals (V_FET). (A–C) Whole-cell current recordings for double-pulse activation of the K⁺ channel from −70 to +50mV (black traces) and with a hyperpolarizing prepulse to −125mV (gray traces) using the (A) Ca²⁺-, (B) Mg²⁺-, and (C) Co²⁺ solutions. The prepulse hyperpolarization slowed the activation of EAG channels. This effect was more pronounced in the presence of Mg²⁺ and Co²⁺. (D–F) Averaged FET signals V_FET (n=50) recorded with a p-channel FET device (D, Ca²⁺; E, Mg²⁺; F, Co²⁺ solution) with (gray traces) and without a hyperpolarizing prepulse (black traces). The FET recordings display two different signals: fast capacitive signals resulting from the stimulation pulse (1, 3) and slower signals due to the current in the cleft between the attached cell membrane and the transistor surface (2). At the end of the stimulus, an instantaneous decline of V_FET (4) that coincides with the negative capacitive transient, and a time-dependent relaxation of the FET signal were observed (5).

We used the following pulse protocol to study the cell-transistor contact: the voltage was first stepped from the holding voltage V_h=from −70 to +50mV. This step probed the fast activation mode of the EAG channel. After returning to V_h, the cell was hyperpolarized (−125mV for 500ms) to promote the transition to the slow activation mode, followed by a short step to V_h (10ms) and then by a step to +50mV to activate the channel. The short step to V_h was applied to compare the capacitive transients of the FET signals. To facilitate comparison, the membrane currents activated without (Figure 2AC, black traces) and with hyperpolarizing prepulses (A–C, gray traces) are superimposed in Fig. 2. In the presence of the Ca²⁺ solution, the hyperpolarizing prepulse had a small but noticeable effect on the rise time of the K⁺ current (Figure 2A, compare black and gray traces). However, in the presence of Mg²⁺ or Co²⁺, the slow activation kinetics became very pronounced (Figure 2BC). Co²⁺ was more effective than Mg²⁺ in slowing channel activation.

Figure 2DF shows FET signals using the Ca²⁺-, Mg²⁺-, and Co²⁺ solutions. To enhance the S/N ratio, the FET recordings were averaged (n=50). The fast transient signals at the onset (Figure 2D, 1) and the offset (3) of the voltage pulses were caused by the coupling of the rectangular stimulation pulses to the capacitance of the attached cell membrane 8,9. The V_FET amplitude reached a steady state during stimulation (2). At the end of the stimulation pulse, an instantaneous decline of V_FET (4) coincides with the negative capacitive transient (3) followed by a slower relaxation of V_FET to the original value (5). Fig. 3 compares the whole-cell patch-clamp currents (black traces) and FET recordings (gray traces) in the presence of the Ca²⁺-, Mg²⁺-, and Co²⁺ solutions. The time courses of the whole-cell currents and the FET signals were similar, except for conditions of fast current activation in the Ca²⁺ solution and fast deactivation due to the rapid closure of the EAG channel.

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Figure 3

Comparison of whole-cell membrane currents and p-channel FET signals (V_FET) for different electrolyte solutions with and without a hyperpolarizing prepulse. (A) Ca²⁺ solution, time course of I_M (black traces) and the corresponding averaged V_FET (n=50) (gray traces). (B) Mg²⁺ solution and (C) Co²⁺ solution. The recordings with a hyperpolarizing prepulse are indicated.

To further investigate the extracellular voltage signals, we used n-channel FETs in addition to p-channel FETs. The higher charge-carrier mobility of n-channel FETs results in a higher transconductance and, in combination with the lower noise level of the buried channel device, in an improved S/N ratio. In contrast to the p-channel FET, n-channel FETs are operated in the first quadrant of the transfer characteristics in which V_GS is positive.

Figure 4A shows a typical whole-cell recording from a HEK 293 cell attached to an n-channel FET. A depolarizing voltage pulse led to fast EAG channel activation. The corresponding V_FET signal is shown in Figure 4B. Due to the significantly higher S/N ratio of the n-channel FET, averaging of signals was not necessary. In fact, the S/N ratio of averaged n-channel recordings (n=25; Figure 4C) was almost as good as that of the patch-clamp recordings. The capacitive transients at the onset (Figure 4B, 1) and at the offset of the stimulus (3), and the increase of the V_FET amplitude to a steady state (2) are readily identified. Similar to p-channel FETs, the signal at the end of the activation pulse displayed two kinetic components: an instantaneous decline of V_FET (4) that coincides with the negative capacitive transient, and a slower relaxation to the initial value (5). The time course of the patch-clamp recording (Figure 4D, black trace) was different from that of the superimposed averaged FET recordings (Figure 4D, gray trace).

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Figure 4

Comparison of whole-cell membrane currents and FET signals V_FET recorded with an n-channel FET. (A) Whole-cell current recording using a Ca²⁺ solution. (B) Nonaveraged n-channel FET signal. The numbers have the same meaning as in Figure 2DF. (C) Averaged FET signal (n=25). The signal/noise ratio of averaged signals is almost as good as that of whole-cell current recordings. (D) Superposition of I_M (black trace) and averaged FET signals (n=25) (gray trace).

We attempted to fit V_FET with a simple equivalent electrical circuit model, the point-contact model (Figure 5A) 10. This circuit was implemented in a standard simulation program for electrical circuits (PSpice 9.1 student version, Cadence Design Systems, San Jose, CA) 30. The circuit consists of capacitors, resistors, and current and voltage sources. The stimulating voltage pulse of the patch-clamp pipette V_M and the whole-cell membrane current I_M were used as voltage and current sources of the simulation circuit (input sources). The model rests on several assumptions.

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Figure 5

Point-contact model of cell-transistor coupling. (A) The equivalent electrical circuit of the point-contact model has been implemented for signal simulation in PSpice. The patch pipette is attached in the whole-cell mode. The cell membrane is divided into free (FM) and attached membrane (JM) with a ratio of 2:1 30 with the respective values of membrane area (A_FM, A_JM) and membrane capacitance (C_FM, C_JM). Hodgkin-Huxley elements (HH) 34 describe the properties of the cell membrane and the voltage-gated EAG channels. C_ox and R_ox=1/G_ox are the capacitance and the resistance of the gate oxide, respectively. V_GS is the applied voltage between gate and source. The gate is set to ground contact (point 0). In the point-contact model, the current at the point contact (point 3) between cell and transistor are summed up according to Kirchhoff’s law. The voltage is applied between point 1 and point 0 (ground contact). The membrane current flows from point 2 to point 0 for the free membrane, and from point 2 to point 3 for the attached cell membrane. A resistor with the conductance g_J from point 3 to point 0 is used to represent the electrical properties of the cleft between the membrane and the transistor. Using the voltage and current signals as input sources, and the respective capacitances and resistances of the patch pipette and the cell membrane, we obtained the simulated FET signals as the voltage V_J between point 3 and point 0. (B) FET recording (black trace) and simulated FET signal (gray trace). We varied g_J, according to Eq. (2) until the simulated signals matched the recorded signals in amplitude and time course.

First, the contact between the cell and the transistor surface is described by a single point. Second, changes in the ion concentration in the cleft between cell and transistor are neglected. Third, both capacitive and membrane currents flow across the conductance G_J in the cleft 30. Fourth, no capacitive current is flowing across the gate; this assumption holds for small signals, because of the high input impedance of the device. Fifth, the seal resistance of the cleft (R_J), with R_J=1 / G_J, is at least two orders of magnitude smaller compared to the resistance of the gate oxide (R_ox=0.1–1 GΩ 31). Therefore, the current across the gate can be neglected in the signal simulation. We further assumed a ratio of 2:1 between the area of free membrane (FM) and membrane in the junction (JM) 30. However, the simulation is largely independent of the FM/JM ratio, because the parameters for all circuit elements have been normalized to the membrane area, i.e., these parameters represent specific values. Even a ratio of 1:1 does not significantly affect the simulated signals 30.

Only a fraction of the total membrane current I_M is flowing across the seal resistance (I_JM=0.33×I_M), resulting in a voltage at the point contact (V_J=R_J×I_JM). In the point-contact model, all currents entering or leaving the contact point are summed up 12:

(1)

In this equation, g_J refers to the specific cleft conductance 13; and refer to the specific conductance of the attached cell membrane and the reversal voltage for the ion species i, respectively, V_M and c_M refer to the applied membrane voltage and the specific membrane capacitance, respectively. According to Eq. (1), changes in the voltage V_J(t) can be caused by both the membrane current and the capacitive current.

We have determined g_J from the capacitive transients observed in the FET recordings (e.g., Figure 2D, 1 and 3) 30:

(2)

We compared the simulated signals V_J (Fig. 6, gray traces) with the p-channel V_FET (Fig. 6, black traces) recorded in different electrolyte solutions (A: Ca²⁺; B: Mg²⁺; C: Co²⁺). The values for the conductance g_J ranged from 0.2 to 3.2 S/cm² (n=28). Similar values have been reported for cell-transistor coupling using hippocampal neurons (g_J=0.6–1.7 S/cm²) 13 and neurons from the brain stem of rats (g_J=0.3–0.9 S/cm²) 30. Under all conditions, the simulation predicts V_J signals that are ∼60% of the total V_FET amplitude (Figure 6AC, left panels). Similar discrepancies have been previously interpreted to be caused by accumulation (or depletion) of ion channels in the membrane area that is attached to the transistor surface 13. The differences between V_FET and V_J (Fig. 6, right panels) show almost no fast FET signal component. Therefore, the point-contact model seems to describe the fast FET signal quite accurately. In fact, the predicted steady-state amplitude is 90±34% (n=28) of the observed fast FET component.

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Figure 6

Comparison of recorded FET signals (V_FET) and simulated FET signals (V_J) (left panels) and differences of V_FET−V_J (right panels). Recorded FET signals (black traces) and simulated FET signals (gray traces) for (A) Ca²⁺-, (B) Mg²⁺-, and (C) Co²⁺ solution. In the right panel, the differences between V_FET and V_J show almost no residual fast component of the FET signal.

Fig. 7 compares patch-clamp recordings and V_FET signals from p-channel (left panels) and n-channel FETs (right panels) using the Ca²⁺ solution. The membrane currents I_M are shown in panel A; the recorded (black traces) and simulated FET signals (gray traces) are shown in panel B; the difference between the recorded and simulated FET signals (V_FET−V_J) is shown in panel C. The waveforms of the V_FET signals from both FET types are qualitatively similar (compare Figure 2 and Figure 4). Both signals embody a fast kinetic component that is well described by the point-contact model that predicts 90±34% (n=28) for the p-channel FETs, and 87±26% (n=7) for the n-channel FETs, and an additional slow component that is not observed in the whole cell current. The difference of V_FET and V_J displays no remaining fast component (Figure 7C). The slow component is significantly larger and slower for n-channel FETs than for p-channel FETs. On average the slow component of the n-channel FET signal is 1.8±0.4 times larger then the respective p-channel FET signal component.

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Figure 7

Comparison of whole-cell membrane currents (I_M) and FET signals (V_FET) recorded with a p-channel FET (left panels) and an n-channel FET (right panels). (A) Whole-cell current. (B) Comparison of averaged V_FET signals (gray traces) and simulated V_J (black traces). The steady-state ratio V_J/V_FET was 60% for the p-channel FET and 25% for the n-channel FET. (C) Difference between recorded and simulated FET signals (V_FET−V_J).

We chose a cell line expressing EAG channels to characterize the mechanism of cell-transistor coupling. The activation kinetics of EAG channels can be manipulated by voltage and divalent cations. We used this system to investigate whether the transistor signal faithfully recapitulates the features of the ionic membrane current. We made the following key observations. First, the response time of the FETs is sufficient to record the fast capacitive transients at the onset and offset of the stimulating pulse. Second, the time course of the transistor signal V_FET is slower than the time course of EAG channel activation in the fast mode, but closely follows the time course of the channel activation in the slow mode. Third, the decline of the transistor signal at the end of the stimulating voltage pulse displays a slow kinetic component that is absent in the instantaneous drop of the whole-cell current. Fourth, n-channel and p-channel transistor signals display distinct time courses. Fifth, the signals of n-channel FETs are significantly larger compared to p-channel signals. Finally, the amplitudes of recorded and simulated transistor signals do not match.

Previous reports explained the discrepancies between recorded and simulated FET signals by the unequal distribution of ion channels between the site of cell-transistor contact and the free membrane 13,14. However, this interpretation neither explains the differences between the n-channel and p-channel FET signals nor the differences in the time course of I_M and V_FET. We reasoned that the V_FET might be affected by changes in ion concentrations in the small cleft between the attached membrane and the semiconductor. The gate oxide of semiconductor devices displays a certain ion sensitivity S_FET. This ion sensitivity is most pronounced for protons, however, K⁺- and Na⁺-sensitivities have been reported as well 25. If the concentration changes in the cleft were substantial, the surface potential of the gate oxide may be altered giving rise to the additional voltage changes.

We estimated the changes in ion concentration in the cleft (δc_j, j=K⁺, Na⁺, and Cl⁻) by solving the coupled Nernst-Planck and Poisson equations (see Appendix ). We assumed a circular attached region with radius R and distance h from the cell surface to the gate oxide. Figure 8B shows the profile of the concentration changes of K⁺, Na⁺, and Cl⁻ that arise in the attached region after a 100-ms injection of K⁺ into the cleft. The concentration change of the ions is largest in the center of the attached region and declines toward the periphery. The overall charge is balanced by concomitant concentration changes of K⁺, Na⁺, and Cl⁻. Considering that the effective gate length of the FET (1–2μm) is significantly smaller than the dimensions of the attached membrane, the question arises to what extent the concentration changes would actually be effective at the gate of the FET. To evaluate this point we integrated the calculated concentration profiles over the cleft volume to obtain a mean In addition, we reasoned that it might be instructive to compare these results with simplified calculations that better approach the idea of the point-contact model (see Appendix ). In the sense of the point-contact model, all ions that diffuse from the cleft to the bulk solution and vice versa have to flow from or to the center of the cleft. We systematically varied the radius R (Figure 9AB) of the attached membrane and the height h of the cleft (Figure 9CD) to estimate the influence of these parameters for the calculated concentration changes. Size and kinetics of critically depend on the dimensions of the attached region. An attached region with larger radius significantly slows down the time course of the concentration changes (Figure 9AB). In contrast, variation in h leads to substantial differences in the steady-state amplitudes of (Figure 9CD). If we compare the concentration changes for K⁺, Na⁺, and Cl⁻ for the spatial integration (Figure 9E) and the point-contact approximation (Figure 9F), we observe significant differences: The simulated are larger and the time course is slower in the point-contact approximation compared to the spatial integration. In fact, the steady-state amplitude of in the point-contact approximation is more than twice the size of the peak δc_j in the center of the cleft when the spatial integration is used (compare Figure 8BF and Figure 9BF). Therefore, we conclude that the point-contact approximation is not sufficient to predict the concentration changes in the cleft.

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Figure 8

Concentration changes in the attached region. (A) Geometry used for the numerical integration. (B) Profile of the change in ion concentration (δc_j) after a 100-ms step injection of K⁺ into the cleft. The following parameters were used for the calculations: cellular holding voltage V_h=+50mV, whole cell K⁺ current I_M=2nA, R=10μm, h=50nm, ratio 2:1 of free/attached membrane, bulk concentrations: [K⁺]=5mM, [Na⁺]=140mM, [Cl⁻]=145mM.

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Figure 9

Concentration changes in the attached region. (A and B) Impact of radius R of the attached membrane on the amplitude and time course of K⁺ concentration changes in the cleft for the spatial integration (A) and the point-contact approximation (B). The values of R are indicated in the figure. The following parameters were used for the calculations: cellular holding voltage V_h=+50mV, whole cell K⁺ current I_M=2nA for 100ms, h=50nm, ratio 2:1 of free/attached membrane, bulk concentrations: [K⁺]=5mM, [Na⁺]=140mM, [Cl⁻]=145mM. (C and D) Impact of cleft height h on the amplitude and time course of K⁺ concentration changes in cleft for the spatial integration (C) and the point-contact approximation (D). Values for h are indicated in the figure; R=10μm. Other parameters as in panels A and B. (E) Time course of for the spatial integration. Parameters as in panels A and B. (F) Time course of for the point-contact approximation. Parameters as in panels A and B; R=10μm.

We now used the model calculations to estimate the slow component of the FET recordings. We calculated by integrating the concentration profiles over the cleft volume, but now we used for the current injection a fraction of the EAG whole-cell currents. Using these values of we determined the potential that reflects the ion sensitivity of the FET device. We only considered the K⁺ sensitivity, because the relative concentration changes of the other ions are small and will not lead to significant potential changes. We experimentally determined the K⁺ sensitivity for the p-channel FET (S_FET=0.7 mV/pK, see Materials and Methods). Unfortunately, for the n-channel FET we were not able to determine the S_FET value due to drift problems during the recordings. In Fig. 9 the simulation of the FET signals are compared with the respective V_FET recording. Here, we combined V_is with the respective V_J from the PSpice simulation. We iteratively adjusted the radius R and the distance h to match the amplitude and kinetics of the slow FET component. For both, the p-channel FET and the n-channel FET, we obtained parameter sets that result in an appreciable simulation of the FET voltage (Fig. 10). For the n-channel FET, we had to additionally assume a slightly higher ion sensitivity to recapitulate V_FET. A closer inspection of the parameter sets reveals that the assumed radius R of the attached membrane (R=19μm) is somewhat above the mean radius of HEK 293 cells. This high value was necessary to approach the kinetics of the slow FET signal component. However, it should be noted that we neglected the possibility that binding of K⁺ to the gate oxide may occur with slow dynamics. No data about these kinetics are available. Therefore, we note that the radius R reported here is an upper estimate. In addition, the height of the cleft is with 39nm for the n-channel FET and 28nm for the p-channel FET at the lower limit of what has been reported for cell-semiconductor distances (12–105nm 14,32,33). As mentioned above, the actual concentration change experienced by the gate of the FET depends on the location of the gate within the attached membrane. In the steady state, and the peak δc_j in the center of the cleft differ by a factor of almost 2 (compare Figure 8BA and Figure 9BA). Our calculations would give larger V_is values when the gate was located in the center of the cleft. In that case, we would obtain larger values of the distance h in our V_FET simulations.

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Figure 10

Comparison of recorded (gray traces) and calculated FET signals (black traces) for a p-channel FET (left panel) and an n-channel FET device (right panel). Each calculated trace represents the sum of the respective PSpice simulation V_J and the additional component V_is due to the ion sensitivity of the FETs. (Left panel) PSpice simulation and results from the spatial integration for the p-channel FET experiment of Fig. 7. Parameters used are: R=19μm, h=28nm, S_FET=0.7mV/pK. (Right panel) PSpice simulation and results from the spatial integration for the n-channel FET experiment of Fig. 7. Parameters used are: R=19μm, h=39nm, S_FET=1.62mV/pK.

In summary, we propose that at least two different mechanisms contribute to the observed FET signals. When channels in the attached membrane open, an electrical signal component is observed, which depends on the seal resistance R_J. The time course of this component closely follows channel activation and deactivation. This component is readily observed as the “fast component” of the FET signal at the end of the activating voltage pulse and can be well described by our PSpice simulation using Eq. (1). We find that the PSpice simulation accounts for 90% (n=28) of the fast component for the p-channel FET and 87% (n=7) for the n-channel FET. Second, for prolonged activation of EAG channels, the ion concentrations in the cleft will change. This gives rise to a change in the surface potential of the gate oxide. This potential rises and declines with a much slower time course than the first, fast component, and explains the slow relaxation of V_FET upon channel closure. However, the differences between n- and p-channel FET signals are not adequately described by these additional potential changes. The amplitudes of the slow component of n-channel FET signals were consistently larger than those for p-channel FETs. Moreover, the signal relaxation after channel closure was slower for n-channel FETs than for p-channel FETs. Our calculations indicate that the ion sensitivity of n- and p-channel FETs may be different. However, we cannot exclude the possibility that other mechanisms contribute to the FET signals. Notwithstanding, our study provides a framework for the understanding of processes at the cell-transistor interface by including diffusional and chemical effects.

Appendix

To estimate the concentration changes of the ions in the cleft between cell and semiconductor, the coupled Nernst-Planck equations, describing the diffusion of the ionic species within an electric field, and the Poisson equation, describing the dependence of the electric field on the net charge distribution, have to be solved simultaneously. The Nernst-Planck equations are given by

(A1)

where the c_j are concentrations, ψ is the electrostatic potential, D_j are diffusion coefficients, z_j electric valences, F and R are Faraday’s constant and gas constant, respectively, T is the temperature, and q_j are source terms. The index j stands for K, Na, or Cl, respectively. The Poisson equation reads

(A2)

where ɛ is the dielectric constant of the solution. The only nonvanishing source term is the potassium influx through the cell membrane into the cleft between cell and FET. The full analysis of this problem is numerically challenging, due to the different timescales of the involved processes charge relaxation and diffusion. To better elucidate that point we rewrite Eq. (A1) in the form

(A3)

where the are the equilibrium bulk concentrations, the δc_j are deviations from these bulk concentrations, and we have replaced the Laplacian of the electric potential by the help of the Poisson equation. In the presence of even slight net charges (nM), the third term in Eq. (A3) becomes by orders of magnitudes larger than the first two terms, leading to a fast charge relaxation towards electroneutrality on a nanosecond timescale. We will employ this fact and will use a reduced integration scheme, which assumes that the fast relaxation towards equilibrium proceeds full way until electroneutrality is reached, thus ignoring the second term in Eq. (A3). Then, the integration can be done in a two-step fashion; for every time step Δt of integration, the injected potassium ions Δt×q_K initiate a fast charge relaxation towards electroneutrality, following the equation

(A4)

after which the dynamics is governed by pure diffusion:

(A5)

This significantly simplifies the numerical evaluation, lifting the need for the explicit computation of the electrostatic potential by solving the Poisson equation. The electroneutrality limit of Eq. (A4) can be found by setting the left-hand side to zero and solving the resulting algebraic problem. A further simplification can be made by ignoring the spatial distribution of different ion concentrations along the cleft radius, and switching to the so-called point-contact approximation by integrating the diffusion equations over the cleft,

(A6)

where are the average concentrations within the cleft, and R is the radius of the cleft. The gradient of the concentrations is approximated by

(A7)

We used both the point-contact model approximation as well as the full integration of Eq. (A5) for modeling and fitting the data. Equation (A5) was solved by a standard finite-element integration scheme, assuming impenetrable boundaries for the cell membrane and the FET surface, and keeping the concentrations fixed at their bulk concentration values (δc_j=0) at the outer boundaries of the integration region (see Figure 8A). The integration region (extracellular space excluding the cleft) was divided into square finite elements of 200-nm edge size; the integration time step was equal to 4μs. In the point-contact approximation, the integration time step was chosen to be 1ms. No changes in the numerical results were discernible when further decreasing finite-element size or integration time step.

Fixed parameters used for the calculations: ɛ=80, T=309.15K, D_K=1.96×10⁻⁵cm²/s, D_Na=1.33×10⁻⁵cm²/s, D_Cl=2.02×10⁻⁵cm²/s.