NANO LETTERS
Modeling the Neuron-Carbon Nanotube-ISFET Junction to Investigate the Electrophysiological Neuronal Activity
2008 Vol. 8, No. 12 4433-4440
Giuseppe Massobrio,† Paolo Massobrio,† and Sergio Martinoia*,†,‡ Neuroengineering and Bio-nanoTechnology Laboratory, Department of Biophysical and Electronic Engineering (DIBE), UniVersity of GenoVa, Via Opera Pia 11a, 16145 GenoVa, Italy, and Neuroscience and Brain Technology Department, Italian Institute of Technology, Via Morego 30, 16163 GenoVa, Italy Received August 1, 2008; Revised Manuscript Received September 16, 2008
ABSTRACT Carbon nanotubes arranged in vertical alignment and normal direction to the gate insulator of an ion-sensitive field-effect transistor are proposed as electrical interfaces to neurons, and a model of such a system is developed to simulate and analyze the electrical interactions and the induced extracellular neuronal electrical activity. The results pointed out nanotubes act on the amplitude and the shape of the recorded signals and promote an increase in the efficacy of neuronal signal transmission.
Carbon nanotubes (CNTs)1 have turned out to be a new way to improve the performances of recording devices: studies showed that CNTs can provide a good surface for neuronal cell adhesion and growth, either on uniform surfaces2 or on isolated CNTs.3-6 Because of the efficient charge transfer between CNTs and surface-anchored molecules, CNTs show high sensitivity to changes of surrounding electrostatic environments. Therefore, CNTs are a promising material for nanoelectronic sensors, e.g., sensors based on nanoscale fabricated structures of CNT field-effect transistors. Such devices have already been explored intensively as chemical and biological sensors.7-11 On the other hand, FET-based devices, such as ionsensitive field-effect transistors (ISFETs),12 can measure the extracellular voltage of a single neuron attached with its cell membrane to the device insulator in an open gate configuration.13-15 The activity of a neuron induces ionic and displacement currents flowing through the membrane, resulting into an extracellular voltage drop along the cleft between the membrane and the gate insulator of the ISFET. The change of the extracellular voltage induced by the neuron gives rise to an electric field across the insulator that modulates the drain-to-source current of the ISFET; this current, changed into a voltage, describes the extracellularly recorded signal probed by the device. Thus, neurons are * Corresponding author. E-mail:
[email protected]. † University of Genova. ‡ Italian Institute of Technology. 10.1021/nl802341r CCC: $40.75 Published on Web 10/29/2008
2008 American Chemical Society
directly connected to ISFETs by a neuro-electronic junction and are characterized by attachment and sealing parameters which play an important part in determining the accuracy of the recorded signal.16,17 In this work, we present a model to investigate the capability of a neuron-CNT-ISFET system to efficiently record the neuronal electrophysiological activity. The system model includes a neuronal cell membrane (simulated by means of a silicon neuron) and an ad hoc modified ISFET which incorporates a bundle (over the insulator gate) of individual CNTs (grown in vertical alignment and in normal direction to the SiO2 gate insulator surface of the ISFET) in such a way that the neuronal cell membrane is in close contact with the nanotubes. Simulations of the recorded extracellular neuronal signals obtained from the neuron-CNTISFET system were carried out, and the results were compared with those obtained from a CNT-free ISFET-based recording device. To this goal, the electronic circuit program HSPICE was used with ad hoc developed and modified models of the neuron, CNT, ISFET, and neuro-electronic junction. We showed that, by varying specific parameters of the CNTs layer and CNT-ISFET junction, different recorded extracellular neuronal signals (both in amplitude and in shape) were obtained for a given input (i.e., for a given simulated action potential). The obtained results pointed out carbon nanotubes, as electrical interfaces to neurons, act both on the amplitude and the shape of the recorded signals and promote an increase in the efficacy of
Figure 1. Equivalent circuit model for two coupled SWCNTs.
neuronal signal transmission. Intriguing limit behaviors of the extracellular signals shape, resembling the intracellular membrane action potential, under specific operating conditions were found and discussed. The neuron model is based on the biophysically inspired silicon neuron circuit proposed by Farquhar and Hasler.18 It revisits channel modeling and gating mechanisms which control the opening and closing of the neuron channels by using the similarities between biological and silicon physics: 19 the fundamental forces causing ion flow in biology are the same fundamental forces causing electron flow in a MOSFET operating at low currents.19,20 Starting from these observations, the Farquhar and Hasler model is a reinterpretation of the voltage-dependent ion channels in a CMOS circuit. The silicon neuron model, whose detailed characterization can be found in ref 18 is computationally efficient and specifically optimized for circuit simulations. Only four MOSFETs and two capacitors are required to model the Na+ channels and only two MOSFETs and one capacitor for K+ channels; one capacitor models the neuron membrane. The activation/inactivation time constants of the Na+ and K+ channels can be easily controlled by acting on the gate bias voltages of the MOSFETs. Carbon nanotubes (CNTs), discovered by Iijima,1 consist of graphene sheets rolled up to form a cylindric molecule. They can be single-walled nanotubes (SWCNTs) or multiwalled nanotubes (MWCNTs), depending on how many walls the tube is made of; moreover, depending on the direction in which CNTs are rolled up (chirality), they show either metallic or semiconducting properties.21,22 Because of their properties of high mechanical and thermal stability, high thermal conductivity, and large current carrying capacity, CNTs have aroused a research interest in their applicability as VLSI interconnects and low-power field-effect transistors.22 However, the high intrinsic ballistic resistance associated with an isolated CNT suggests the use of a bundle of CNTs conducting current in parallel, thus reducing the impedance of the devices and providing a high drive current. Figure 1 displays the RLC equivalent circuit model for two coupled SWCNTs, which is based on the Luttinger liquid model for individual SWCNTs presented in ref 23 and we used in the simulations. Each SWCNT in the circuit model is made up of lumped resistors24-26 representing both the intrinsic ballistic resistance RI and an additional contact resistance RC between the SWCNTs and on-chip metal 4434
components. A distributed resistance24-26 RO takes into account the ohmic resistance of the SWCNT which is determined by the nanotube length and the mean free path of acoustic-phonon scattering when low-bias voltages (as in the case considered in this work) are applied; moreover, a coupling resistance27 RCoupl takes into account the resistance between neighboring SWCNTs. The capacitors23,28-32 (per unit length) CQ, CE, and CCoupl represent the quantum capacitance of the SWCNT, the electrostatic capacitance to ground, and between SWCNTs, respectively. The expression of the electrostatic capacitance CE was then adapted, following the works of refs 33 and 34, to take into account the arrangement, considered in this work, where SWCNTs are surrounded by an electrolyte solution (NaCl). The inductors23,28-32 (per unit length) LK and LM model the kinetic and magnetic inductances of the SWCNT, respectively. Finally, as there is no ground plane in the considered SWCNTs arrangement, the distance y of the SWCNT away from the ground plane affecting the equations of the above-mentioned parameters was replaced by the length lcnt of the SWCNT itself.23 For a description from a theoretical physics point of view (complementary to the circuit description presented here) of each component, the reader is referred to the cited references and references therein. Referring to the RLC equivalent circuit of the SWCNT of Figure 1, two SWCNT impedances can be defined, i.e., the impedance of the isolated SWCNT ZCNT )
RCNT + jωLCNT ( jω) LCNTCCNT + jωRCNTCCNT + 1 2
(1)
and the coupling impedance between two SWCNTs ZCOUPL )
RCoupl - jωR2CouplCCoupl (ωRCouplCCoupl)2 + 1
(2)
Equations 1 and 2 have to be evaluated in the neuron action potential frequency range. In the above equations, RCNT ) (RI + RC + RO) is the total resistance, LCNT ) (LM + (LK/4)) is the total inductance per unit length, and CCNT ) ((4CECQ)/(CE + 4CQ)) is the total capacitance per unit length of the SWCNT; RCoupl and CCoupl are the coupling resistance and capacitance per unit length between two SWCNTs, respectively, each of diameter dcnt, length lcnt, laid out at a distance x between their centers. Different approaches were proposed to calculate the number of nanotubes in a given bundle. In this work, we followed the approach proposed in ref 31. Thus, a SWCNTbundle is assumed to be composed of hexagonally packed identical SWCNTs, each of them is surrounded by six immediate neighbors, with their centers uniformly separated by a distance x. The “densely” packed bundle with x ) dcnt will lead to best interconnect performance (all SWCNTs of the bundle show metallic properties). On the other hand, the condition of the presence of nonmetallic SWCNTs (not contributing to current conduction) can be taken into account by considering “sparsely” packed bundles (x > dcnt). If nw and nl are the number of “rows” and “columns” of the SWCNTs in the bundle, respectively, defined as31 Nano Lett., Vol. 8, No. 12, 2008
nw ) nl )
the total number ncnt expressed as31
wb - dcnt x
(3a)
lb - dcnt
+1 (3b) √3 x 2 of SWCNTs in a bundle can be
nl for nl even 2 nl - 1 for nl odd ncnt ) nwnl 2 ncnt ) nwnl -
(4a) (4b)
In eqs 3a and 3b, wb is the bundle width, lb is the bundle length, x is the inter-SWCNTs distance, and the symbolism indicates the larger integer less than or equal to the argument. For the considered layout (SWCNTs grown in vertical alignment and in normal direction to the SiO2 gate insulator surface of the ISFET), the bundle height coincides with the SWCNT length lcnt. Ion-sensitive field-effect transistors (ISFETs)12,35 are MOSFETs without the gate metallization which use an exposed gate insulator (e.g., SiO2, Si3N4, Al2O3, Ta2O5) to measure ion concentrations or local changes of charge densities in electrolyte solutions. The developed model36 of the ISFET assumes such device as two fully uncoupled stages (from the physical point of view): an electrochemical stage (the electrolyte-insulator interface) modeled by the theory of the electrical double-layer and site-binding37 and an electronic stage (the MOSFET which is the basic structure of the ISFET) modeled according to the MOSFET theory. The approach36,38 we followed led to an ISFET equivalent circuit made up of an open gate MOSFET with two capacitors in series which model the Helmholtz (CHelm) and the diffuse (CGouy) layers, i.e., the polarization layers of the electrolyte solution in front of the ISFET gate insulator. Moreover, a voltage source modeling the reference electrode, and a “chemical” connection allowing specifying an input chemical signal as an independent voltage source (i.e., the pH value) that controls the electrolyte-insulator potential were also considered in the equivalent circuit36 of the ISFET. The developed ISFET model was used as a “substrate device” for SWCNTs to detect (model) the electrical activity of neurons “grown” on it. The proposed equivalent circuits of the neuron-ISFET and neuron-CNT-ISFET junctions, based on a biophysical approach, were highlighted in the schematic of Figure 2 (cf. yellow boxes). The meaning of the circuit model components is summarized below; moreover, the expressions which define each component were tailored to the considered simulated configuration where the neuronal patch was assumed to cover entirely the “recording sensitive area” of the ISFET gate insulator and of the top-surface of the SWCNT bundle. Rseal (seal resistance between the cell and the “recording sensitive area” of the underlying recording device) models how much the cell is attached to the ISFET and/or SWCNT bundle, that is, it describes the separation of the neuron and Nano Lett., Vol. 8, No. 12, 2008
Figure 2. Schematic of two neurons, each coupled in a one-to-one correspondence to one SWCNTBundleISFET and one ISFET. This schematic was used for the simulations. (In the text, the suffixes 1 and 2 identify the ISFET with CNTs and the CNT-free ISFET, respectively). The parameters dng1 and dng2 are the average neuronto-SWCNT bundle top-surface and neuron-to-ISFET gate insulator distances, respectively. The other components Chd, Rseal, Rspread, ZCOUPL, and ZCNT (cf. main text for their mathematical formulation) highlighted in the yellow boxes define the neuron1-CNT-ISFET1 junction (SN1) and the neuron2-ISFET2 junction (SN2).
the “recording devices sensitive areas” which results in an extended cleft of electrolyte. It is in parallel to the ISFET gate insulator and/or SWCNT bundle top-surface and it depends on the electrolyte type, on the distance between the neuron and the recording sensitive area, and on the percentage of sensitive area covered by the cell. It is defined as16,17,39 Rseal )
Fs δ dng
(5)
In eq 5, Fs is the resistivity of the electrolyte solution (for normal saline Fs ) 0.7 Ω m), dng is the average neuron-toISFET gate insulator or neuron-to-SWCNT bundle topsurface distances, δ is a surface overlapping coefficient which takes into account the percentage of sensitive area covered by the neuron. Its expression was evaluated depending on the different layouts involving the neuron, ISFET gate insulator, and SWCNT bundle top-surface areas. In particular, for the considered simulation configuration, Rseal results into the series of two components: one (Rseal1) affecting the SWCNT bundle top-surface (dng ) neuron-to-SWCNT bundle top-surface distance, δ1 ) (Abundle/Agate)), and one (Rseal2) affecting the gate insulator sensitive surface surrounding the SWCNT bundle (dng ) neuron-to-ISFET gate surface distance, δ2 ) (Agate - Abundle)/Agate, δ2 ) 1 for a CNT-free ISFET), with Abundle and Agate being the SWCNT bundle topsurface area and the ISFET gate insulator area, respectively. Rspread (spreading resistance) models the signal loss due to the distance between the neuron and the ISFET gate insulator surface and/or the SWCNT bundle top-surface, and it is placed perpendicularly to their recording sensitive surfaces. For the considered simulation configuration, Rspread is the parallel of two components as for Rseal. According to 4435
ref 40, referring to the SWCNT bundle of length lb and width wb (wb > lb), the expression of the Rspread component can be written as
( )
Fs ln 4 Rspread )
wb lb
(6a)
πwb
Similarly, referring to the ISFET gate of length Lisfet and width Wisfet (with an adhered SWCNT bundle of length lb and width wb), the expression of Rspread component can be written as
(
Wisfet - wb Fs ln 4 Lisfet - lb Rspread ) π(Wisfet - wb)
)
(6b)
For CNT-free ISFETs, only eq 6b holds and lb and wb have to be set at zero. Chd (neuron membrane-to-electrolyte capacitance) models the polarization layers of the electrolyte solution in front of the neuron surface toward the SWCNT bundle top-surface and the ISFET gate insulator surface. It is the series of the Helmholtz layer capacitance CHelm )
(εIHPεo)(εOHPεo) A (εOHPεo)dIHP + (εIHPεo)dOHP cont
(7)
and the Gouy-Chapman or diffuse layer capacitance CGouy )
q√2εrεokTCbulk Acont kT
(8)
In eqs 7 and 8, εIHP and εOHP are the inner and outer Helmholtz plane relative dielectric constants, respectively; εo is the dielectric permittivity of free space; dIHP is the neuron to nonhydrated ion distance; dOHP is the neuron to hydrated ion distance; εr is the diffuse layer relative dielectric constant; k is the Boltzmann’s constant; T is the absolute temperature; q is the electron charge; Cbulk is the bulk concentration; Acont ) (δAgate(bundle)) is the contact area between the neuron and the ISFET gate insulator or the SWCNT bundle top-surface. In particular, for the considered simulation configuration, Chd is the parallel of two components (each made up of the series of Helmholtz and diffuse layers capacitance, eqs 7 and 8), as for Rseal. The aforementioned parameters are common to both the junctions. Moreover, the behavior similarity of the two junctions led us to assume the neuron1-CNT-ISFET1 junction as an “extension” of the circuit modeling the neuron2-ISFET2 junction. To translate the “extension” concept into electrical components which model the presence of the carbon nanotubes as electrical interfaces to neurons, we referred to the experimental results (extracellular signal shapes) indicated in refs 3 and 5 and to the properties of the nanotubes which were demonstrated to provide a good surface for neuronal cell adhesion and growth.2-5 These considerations drove us to assume the extracellular signal shapes recorded in the presence of the SWCNTs bundle could be thought of as induced by a high-valued, SWCNT-dependent seal-like resistance, thus considering that distances between neuronal membrane and SWCNT-bundle can go down to few nanom4436
eters. This assumption suggested us to split the SWCNT bundle impedance into two components, i.e., (a) a bundle Bundle coupling impedance (ZCOUPL ) placed in parallel to the SWCNT bundle top-surface (neuron membrane) and which appears in parallel to Rseal in conditions of weak-coupling or alone in conditions of strong-coupling (Rseal f ∞) and (b) a bundle CNT impedance (ZBundle CNT ) placed perpendicularly to the SWCNT bundle top-surface (neuron membrane) which appears in series to Rspread. The equivalent SWCNTs bundle coupling impedance was defined as Bundle ZCOUPL ) (nl - 1)(nw - 1)ZCOUPL
(9)
and the equivalent bundle SWCNT impedance was defined as Bundle ZCNT )
ZCNT ncnt
(10)
where ZCNT and ZCOUPL are given by eqs 1 and 2, respectively, and the total number ncnt of SWCNTs in the bundle is evaluated by eqs 4a and 4b. We took into account the configurations sketched in Figure 2: two neurons, each stimulated by 5 nA time-delayed current impulse sources, were coupled to one SWCNTBundleISFET1 and one ISFET2 in a one-to-one correspondence. Yellow boxes of Figure 2 highlight the neuron1-CNT-ISFET1 junction (SN1), and the neuron2-ISFET2 junction (SN2). In order to model the spatial propagation of the action potential along the neuron and to take into account how different sealing conditions could influence the signals recorded by the SWCNTBundleISFET1 and by the ISFET2, the neuron membrane was simulated according to the compartmental approach.41 Practically, the neuron is disassembled into regions or compartments of membrane small enough to be considered isopotential which, therefore, may be represented, in its simplest configuration, by a membrane capacitance in parallel with a membrane resistance. Series resistors connect adjacent compartments. The advantage of this approach is that it places no restrictions on the membrane properties of each compartment (e.g., compartments may be passive or excitable) or on the geometry of the neuron. In particular, in our simulations, we considered the neuron split up into three isopotential compartments, each modeled by the silicon neuron model previously described, and characterized by the same electrical properties. In this way, the signals recorded by the SWCNTBundleISFET1 and by the ISFET2 come out of one of these compartments with different adhesion conditions. All the simulations were performed at constant temperature T ) 310 K. Moreover, to better appreciate the influence induced by the presence of SWCNTs on the neuronal extracellular signals recorded by SWCNTBundleISFET1 and to compare these results with those obtained by ISFET2, we assumed all the bioelectronic devices (i.e., neurons, ISFETs, neuro-electronic junctions) of the configurations of Figure 2 were identical. However, nothing prevents us from assuming different morphologies for the neurons or different geometric or physical-chemical configurations for the ISFET or SWCNT: it is enough to specify the new pertinent parameter values into the input file of HSPICE. Nano Lett., Vol. 8, No. 12, 2008
The neurons interfacing the SWCNTBundleISFET1 and the ISFET2 were represented by a compartment characterized by diameter φn ) 16 µm, and membrane capacitance Cmem ) 1 µF/cm2. A physiological medium made of NaCl 150 mM was considered. The MOSFET models of the “silicon neuron” circuits were based on the HSPICE EnzKrummenacher-Vittoz (EKV) model42 running in the subthreshold regime and characterized by parameter values set for standard 0.5 µm CMOS technology. The equations which define the carbon nanotube model were implemented in HSPICE and internally evaluated by the specified input parameters. The SWCNTs were assumed to be in a “densely” packed structure (x ) dcnt), grown in vertical alignment and in normal direction to the SiO2 gate insulator surface of the ISFET. Each SWCNT was characterized, in the “reference simulation”, by the following set of parameter values: length lcnt ) 80 nm, diameter dcnt ) 3 nm, relative dielectric constant of the medium (NaCl) surrounding the SWCNT εr ) 78.5, relative magnetic permeability µr ≈ 1 (considered nonmagnetic), molar concentration of the electrolyte Cbulk ) 150 mM, nominal contact resistance Rcnom ) 20 kΩ, and electronic mean free path λap ) 2.8 µm for the considered SWCNT diameter.24,25 The bundle geometry was assumed to be lb ) 220 nm (bundle length which can reach at maximum Lisfet), wb ) 300 nm (bundle width which can reach at maximum Wisfet). The above SWCNT parameter values introduced in HSPICE, yielded ncnt ) 8274, ZCOUPL ) 64.34 kΩ, and ZCNT ) 26.45 kΩ. The MOSFET of the electronic stage of the ISFET model was assumed to be a metal-free depletion type p-channel device; the nominal length and width of the channel were Lisfet ) 3.4 µm and Wisfet ) 6.0 µm, respectively, and the thickness of the SiO2 gate insulator was tox ) 50 nm. Depletion type MOSFET allowed us to take out the bias voltage source between the ionic solution and the silicon, necessary to put the MOSFET into conduction mode. Actually, this bias contributes to drift currents because of the ion migration in the device dielectric layers: these drift currents are a potential source for noise, device degradation by electrochemical corrosion effects, and damages to the cultured neurons.43 Moreover, the use of a p-channel rather than an n-channel device exhibits a reduced 1/f noise. Simulations were carried out by considering the driving condition for the drain-source voltage VDS ) -2.5 V. As stated before, the change of the extracellular voltage induced by the neuron gives rise to an electric field across the insulator that modulates the drain-to-source current of the ISFET; this current, changed into a voltage, describes the extracellularly recorded signal probed by the device. Thus, the drain-to-source currents IDS of the ISFETs, obtained from the simulations, were fed into current-voltage converters:44 the changes of IDS were then converted into changes of the extracellular voltage Vextr. Moreover, the electrolyte bath between the neurons and SWCNTBundleISFET1 and ISFET2 was kept at pH ) 7.4, thus assuming no acidification effect could be induced by the cell coupled to the recording devices during simulations. Nano Lett., Vol. 8, No. 12, 2008
The equations which model the neuro-electronic junctions were implemented in HSPICE and automatically evaluated by the specified input parameters. As already mentioned, the two neurons of Figure 2 were considered identical. Assuming εIHP ) 16, εOHP ) 32, εr ) 78.5, dIHP ) 0.1 nm, dOHP ) 0.4 nm, Fs ) 0.7 Ω m, Cbulk ) 150 mM, T ) 310 K, (eqs 1-8) yielded Rspread,SN1 ) Rspread,SN2 ) 72.56 kΩ, and Chd,SN1 ) Chd,SN2 ) 6.24 pF. The subscripts SN1 and SN2 refer to the neuron1-CNT-ISFET1 and neuron2-ISFET2 configuration paths indicated in Figure 2, respectively. The value of Rseal was assumed as a fitting parameter by varying the average neuron-to-SWCNTBundleISFET1 bundle top-surface and/or neuron-to-ISFET2 gate insulator distances dng. Referring to Figure 2, we considered for the “reference simulation” the following values: dng1 ) 4 nm (thus, the distance of the neuron from the gate surface surrounding the SWCNT bundle will result in (dng1 + lcnt) ) 84 nm) and dng2 ) 80 nm, corresponding, from eq 5, to Rseal,SN1 ) 8.87 MΩ (δ1 ) 3.235 × 10-3, δ2 ) 0.9968) and Rseal,SN2 ) 8.75 MΩ (δ2 ) 1). Bundle Moreover, eqs 9 and 10 yielded ZCOUPL ) 523.4 MΩ and Bundle ZCNT ) 3.2 Ω. Simulations of the behavior of the two circuit configurations of Figure 2 were carried out using HSPICE. The models, the parameters values, and the adhesion conditions indicated in the previous sections were associated with each pertinent component to define the “reference simulation”. Under these simulation conditions, the intracellular action potentials of the neurons (neuron1 and neuron2) are shown in Figure 3a. Figure 3b points out the corresponding simulated extracellular potential signals of the neurons (neuron1 and neuron2) transduced by SWCNTBundleISFET1 and ISFET2, respectively. It should be noticed that even if the coupling has a strong capacitive contribution (mediated by Chd and by the input ISFET capacitance), the incoming Chd current consists of the (capacitive) membrane current and of the ionic currents (passive and voltage-gated) flowing through the cell membrane. Right away, the analysis of the outputs of the “reference simulation” shown in Figure 3b could induce one to think that the presence of the SWCNT bundle does not influence the recorded extracellular neuronal signals. Really, the similarity of the extracellular signals (for the actual considered configuration) can be explained by assuming that the influence of the SWCNT bundle (number of SWCNTs ncnt ) 8274) is not sufficient yet to overcome the influence of the underlying ISFET gate area. As from now, the SWCNTs number seems to play an important part in the signal control: its marked influence on the extracellular signals will be pointed out later on. The dependence of the extracellular neuronal signals recorded by the SWCNTBundleISFET1 on the adhesion conditions was investigated by varying the parameters defining Rseal, Chd, and Rspread. In particular, the simulation results (data not shown) obtained by sweeping Rseal by the neuron1-to-ISFET1-SWCNTBundle top-surface distance dng1 (from a strong-coupling condition (dng ) 10 nm) to a weakcoupling condition (dng ) 500 nm)) bore out the 1/dng1 dependence of the recorded extracellular signals as in the 4437
Figure 3. HSPICE simulation results. (a) Action potentials of neuron1 and neuron2. The reference baseline potential was set to 0 for convenience (ac-coupled model). (b) Extracellular potential signals transduced by SWCNTBundleISFET1 and ISFET2. The adhesion conditions are defined by the following main parameters: Rseal,SN1 ) 8.87 MΩ (δ1 ) 3.235 × 10-3, δ2 ) 0.9968), Rseal,SN2 ) 8.75 MΩ (δ2 ) 1), Rspread,SN1 ) Rspread,SN2 ) 72.56 kΩ, Chd,SN1 ) Bundle ) 523.4 MΩ, and ZBundle ) 3.2 Ω. Chd,SN2 ) 6.24 pF, ZCOUPL CNT
case of a CNT-free ISFET-based recording device.17 Moreover, Chd (data not shown) variations give rise to similar dependence of the waveforms of the extracellular potential signals by acting on the signal amplitude. No significant modifications of the extracellular signal shape were obtained by varying, also within a wide range, the value of Rspread. As already mentioned, the SWCNTs number seems to be a key parameter in the signal control: thus, we turned our attention to the effects induced on the extracellular signals by the SWCNT number in the bundle. This goal can be achieved by independently varying (a) the length lb and width wb of the bundle (the bundle height coincides with the SWCNT length), (b) the SWCNT diameter dcnt, and (c) the inter-SWCNT distance x which induces a “sparsely” packed bundle arrangement out of the present investigation. Thus, assuming a “densely” packed bundle arrangement (interSWCNTs distance x ) dcnt) and assuming the “reference simulation” conditions still hold, we varied first the bundle length lb and width wb (bundle area) which affect eqs 3a, 3b, 4a, and 4b. Thus, simulations were carried out for the following pairs of bundle length lb and width wb: (220 nm, 300 nm), (500 nm, 500 nm), (800 nm, 800 nm), (1.0 µm, 2.0 µm), (2.0 µm, 4.0 µm), and (3.3 µm, 5.9 µm), resulting in values of ncnt ranging from about 8.2 × 103 to about 2.5 4438
Figure 4. HSPICE simulation results. (a) Extracellular potentials of the neurons neuron1 and neuron2 transduced by SWCNTBundleISFET1 and CNT-free ISFET2, respectively, as a function of the top-surface geometry of the SWCNT bundle (resulting into the SWCNTs number in the bundle), as explained in the text. The label (S) in the graph indicates the bundle top-surface area value, namely: S1 ) (lb ) 220 nm × wb ) 300 nm); S2 ) (lb ) 500 nm × wb ) 500 nm); S3 ) (lb ) 800 nm × wb ) 800 nm); S4 ) (lb ) 1.0 µm × wb ) 2.0 µm); S5 ) (lb ) 2.0 µm × wb ) 4.0 µm); and S6 ) (lb ) 3.3 µm × wb ) 5.9 µm). It is evident the extracellular signal shape (recorded by the SWCNTBundleISFET1) which resembles the intracellular membrane action potential at large bundle top-surface areas, corresponding to large numbers of SWCNTs. In such a configuration, the gate insulator surface is almost completely covered by SWCNTs. (b) Peak-to-peak extracellular signal amplitudes (recorded by the SWCNTBundleISFET1 and CNT-free ISFET2) as a function of the SWCNTs number in the bundle.
× 106, Rseal,SN1 from about 8.9 MΩ to about 167.4 MΩ, Bundle ZBundle COUPL from about 523.4 MΩ to about 160.3 GΩ, and ZCNT from about 3.2 Ω to about 10.5 mΩ. The other parameters kept the values obtained in the “reference simulation” because of their independence of the bundle area variations (SWCNTs number). The HSPICE simulated extracellular signals obtained by varying the bundle area were shown in Figure 4a. Additionally, in Figure 4b the peak-to-peak extracellular signal amplitudes as a function of the SWCNTs number in the bundle were plotted. The influence of the SWCNT bundle dimensions (i.e., the SWCNT number) on the shapes of the extracellular neuronal signals (compared with the signals “recorded” by ISFET2) is evident and bears out the trend indicated in the literature: the proposed model predicts response amplitude larger than that recorded by the ISFET without carbon nanotubes. Moreover, from the simulations, a value of ncnt is found, Nano Lett., Vol. 8, No. 12, 2008
Figure 5. HSPICE simulation results. Extracellular potentials of the neuron1 transduced by the SWCNTBundleISFET1 for three values of the SWCNT diameter dcnt (dcnt ) 3.0, 20.0, and 50.0 nm). It is evident the damping of the extracellular signal amplitude as a consequence of the reduced SWCNTs number in the bundle because of the increased carbon nanotubes diameter.
beyond which the expected recorded extracellular signal shape changes, resembling the intracellular membrane action potential. After an initial increase of the extracellular signal amplitude keeping up the increase of ncnt, both a limit amplitude value and an intracellular potential-like waveform were obtained, reaching a saturation condition when the ISFET gate sensitive area was entirely covered by the carbon nanotubes. The saturation behavior and the action potential-like shape, on the same ncnt value and distance dng, can be altered by acting on the more-sensitive parameters influencing the extracellular signals (e.g., by lowering the Chd value). A possible attempt of explanation of this intriguing behavior might induce one to speculate that the resulting high-valued equivalent sealing resistance behaves as if the recording sensitive element SWCNTBundleISFET1 was “embedded” within the neuron membrane itself, thus recording an intracellular-like rather than an extracellular potential. This is also reflected by changes in amplitude (cf., Figure 4b), pointing out nonlinear filtering of the original electrophysiological signal. Under the “densely” packed bundle arrangement and the “reference simulation” conditions, we carried out simulations also by sweeping the value of the SWCNTs diameter dcnt from 3 to 50 nm, resulting into values of ncnt ranging from about 8.2 × 103 to 18, ZBundle COUPL from about 523.4 MΩ to about Bundle 461 kΩ, and ZCNT from about 3.2 Ω to about 1.5 kΩ; Rseal,SN1 kept the value obtained in the “reference simulation” of about 8.9 MΩ because of its independence of the SWCNTs diameter. The HSPICE simulated extracellular signals obtained by varying the SWCNT diameter were shown in Figure 5. It is evident that the attenuation of the extracellular signal amplitude is a function of an increase of the carbon nanotubes diameter as a consequence of the reduced SWCNTs number in the bundle. Finally, simulations (data not shown) of the extracellular neuronal signals recorded by SWCNTBundleISFETs as a function of the SWCNT length lcnt were performed. The simulations were carried out by considering a wide range of Nano Lett., Vol. 8, No. 12, 2008
lcnt values and by keeping the bundle configuration and all the other parameters at their values of the “reference simulation”. The results showed that by increasing lcnt values, the recorded extracellular signals decrease in amplitude, thus pointing out a weak-coupling condition. This behavior has to be ascribed mainly to Rseal2 (dng ) neuron-to-ISFET gate surface distance ) neuron-to-SWCNT bundle top-surface distance + SWCNT length), with Rseal1 independent of lcnt Bundle and ZCOUPL weakly affected by lcnt. Carbon nanotubes were used as electrical interfaces between neurons and ISFETs, and a model of such a hybrid system was developed to simulate and analyze the electrical interactions and the induced extracellularly recorded neuronal electrical activity. Efficient models of the neuron, SWCNT bundle, and ISFET were implemented in HSPICE as functional electronic macromodels. These models were then used to simulate the extracellular neuronal signals delivered by a simple network configuration made up of two neurons, each coupled to one SWCNTBundleISFET (the carbon nanotubes were assumed to be grown in vertical alignment and in normal direction to the SiO2 gate insulator surface of the ISFET), and to one CNT-free ISFET, in a one-to-one correspondence. The neuronal electrical activity was simulated as a function of the neuro-electronic junction parameters (seal resistance, double-layer capacitance, and other general adhesion conditions), and of the SWCNT properties (diameter, length, number in the bundle, bundle geometry, distance from neurons). From the simulations, useful information on the shape of the recorded neuronal signals also under limitconditions (weak and strong coupling) were obtained: the carbon nanotubes affect both the amplitude and the shape of the recorded signals, matching the theory and the equations defining the models, and turning out potential devices able to improve neural signal transfer. The intriguing limit behavior of the extracellular signals, resembling the intracellular membrane action potential, obtained under specific operating conditions, should be experimentally verified. A possible explanation of this behavior lies in the possibility to achieve a very tight coupling between CNTs and cell membrane, approaching a condition similar to a cell-attached situation for whole cell patch-clamp measurements,45 thus favoring a very efficient signal transduction. Finally, even if the proposed model and the presented results concerned the considered neuron-SWCNTBundleISFET junction configuration, the results of this work could be conveniently extended to other biorecording devices including array-based systems for both in vivo and in vitro applications. References (1) Iijima, S. Nature 1991, 354, 56–56. (2) Mattson, M. P.; Haddon, R. C.; Rao, A. M. J. Mol. Neurosci. 2000, 14, 175–182. (3) Gabay, T.; Ben-David, M.; Kalifa, I.; Sorkin, R.; Abrams, Z. e. R.; Ben-Jacob, E.; Hanein, Y. Nanotechnology 2007, 18. (4) Gabay, T.; Jakobs, E.; Ben-Jacob, E.; Hanein, Y. Physica A 2005, 350, 611–621. (5) Mazzatenta, A.; Giugliano, M.; Stephane, C.; Gambazzi, L.; Businaro, L.; Henry, M.; Prato, M.; Ballerini, L. J. Neurosci. 2007, 27 (26), 6931–6936. (6) Lovat, V.; Pantarotto, D.; Lagostena, L.; Cacciari, B.; Grandolfo, M.; Righi, M.; Spalluto, G.; Prato, M.; Ballerini, L. Nano Lett. 2005, 5, 1107–1110. 4439
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