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Predicting and rationalizing the effect of surface charge distribution andorientation on nano-wire based FET bio-sensors†
Luca De Vico,*a Lars Iversen,bc Martin H. Sørensen,d Mads Brandbyge,d Jesper Nyg�ard,ec Karen L. Martinezbc
and Jan H. Jensen*a
Received 25th March 2011, Accepted 19th May 2011
DOI: 10.1039/c1nr10316d
A single charge screening model of surface charge sensors in liquids (De Vico et al., Nanoscale, 2011, 3,
706–717) is extended to multiple charges to model the effect of the charge distributions of analyte
proteins on FET sensor response. With this model we show that counter-intuitive signal changes (e.g.
a positive signal change due to a net positive protein binding to a p-type conductor) can occur for
certain combinations of charge distributions and Debye lengths. The newmethod is applied to interpret
published experimental data on Streptavidin (Ishikawa et al., ACS Nano, 2009, 3, 3969–3976) and
Nucleocapsid protein (Ishikawa et al., ACS Nano, 2009, 3, 1219–1224).
1 Introduction
Nano-BioFET sensors1–5 are made of electrically contacted,
semiconducting nano-wires working as field effect transistors
(FET), which can sense binding events taking place at their
surface. A bio-functionalization layer is linked to the surface of
the nano-wire and is responsible for the recognition of the ana-
lyte of interest. The analyte immobilization creates a change in
the charge distribution in proximity to the surface (modulated by
the ionic species present in solution through a Debye screening),6
with a consequent perturbation of the current flow in the nano-
wire. Nano-BioFET sensor importance lies in (i) the high binding
selectivity inherited from the bio-molecules constituting the bio-
functionalization layer, (ii) the absence of a need to label the
analyte or receptor, and (iii) the high sensitivity for analytes with
concentrations as low as femto molar.7,8
While theoretical models of nano-BioFETs are available,8–15
most interpretations of experimentally observed signal changes
are done by using what can be called a single charge model: it is
aDepartment of Chemistry, University of Copenhagen, Universitetsparken5, DK-2100 Copenhagen, Denmark. E-mail: [email protected];[email protected]; Fax: +45 35 32 02 14; Tel: +45 35 32 02 39bBio-Nanotechnology Laboratory, Department of Neuroscience andPharmacology, University of Copenhagen, Universitetsparken 5,DK-2100 Copenhagen, DenmarkcNano-Science Center, University of Copenhagen, Universitetsparken 5,DK-2100 Copenhagen, DenmarkdDTU Nanotech, Department of Micro and Nanotechnology, TechnicalUniversity of Denmark, DTU-Building 345 East, DK-2800 KongensLyngby, DenmarkeNiels Bohr Institute, University of Copenhagen, Universitetsparken 5,DK-2100 Copenhagen, Denmark
† Electronic supplementary information (ESI) available: A detaileddescription of the SMSCSL model is given, along with the Streptavidinand N protein treatment. Additional material is provided in Tables1S–3S and Fig. 1S–13S. See DOI: 10.1039/c1nr10316d
This journal is ª The Royal Society of Chemistry 2011
verified that the direction of the signal is the one expected based
on the total charge of the analyte, taking into account whether
the nano-wire is an n- or p-type semiconductor (e.g. a decrease in
conductance due to a negative analyte binding to an n-type nano-
wire). This assumption works satisfactorily in many cases, and
we have recently shown that the single charge model can also
form the basis for a semi-quantitative interpretation of the
magnitude of the nano-wire conductance signal change and its
dependence on various experimental conditions, such as ionic
strength and pH.16
However, a few reports have emerged where the observed
signal change did not have the expected direction based on the
total charge of the protein analyte.17,18 One possible reason for
this is that the total charge of the protein is too simple a repre-
sentation of the effect of the many charged groups distributed
throughout the protein, which are subject to different screening
effects from the buffer ions depending on their different distances
from the nano-wire surface. To test this hypothesis an improved
model is needed.
In this paper we (i) present an extension of our single charge
model for nano-BioFET conductance sensitivity16 to multiple
charges, (ii) demonstrate under which conditions it is possible to
expect counter-intuitive changes in the sign of the signal, by
considering a few prototypical charge distributions, and (iii)
apply the multiple charges method to the interpretation of
experimentally observed signal changes that cannot be explained
by the single charge model.
2 Computational methodology
In the current method we want to predict the change in
conductance sensitivity
�DG
G0
�when N systems (biomolecules)
with m charged groups are sensed close to the surface of
Nanoscale, 2011, 3, 3635–3640 | 3635
a nano-BioFET. The computational method (multiple charges
model) is based on the description of the BioFET that builds on
a screening model of surface charge sensors in liquids (SMSCSL)
given various parameters, as described elsewhere.16,19 A short
summary is also provided as Supplementary Information.† The
value of the conductance sensitivity is computed as:
DG
G0
¼ � 2
Rep0G
"Xmi
ðGlisbi Þ#
(1)
where R is the radius of the nano-wire, e the elementary charge,
p0 the nano-wire charge carrier (hole) density.20 G and Gl are
dimensionless functions quantifying the actual sensitivity of the
nano-wire. Their definition is given as Supplementary Informa-
tion eqn (S4) and (S6).† In brief, they depend on the buffer
solution ionic strength through the Debye screening length lD(eqn (S8)†),6 the nano-wire Thomas–Fermi distance lTF (eqn
(S11)†), the relative permittivities of the nano-wire, the oxide
layer and the buffer (31, 32 and 33, respectively), and the oxide
layer thickness DR. Ref. 16 shows how each parameter influences
the computed signal.
Each of the N simulated biomolecules is represented by m
charged groups. For each group i with charge Qi and separated
from the nano-wire surface by a distance li, the value of Gl is
computed using eqn (S6).† The corresponding surface charge
density is computed as:
sbi ¼NQi
2pðRþ DRþ liÞL (2)
where L is the length of the nano-wire. Fig. 1 summarizes the
various parameters and their physical meaning.
3 Results and discussion
3.1 Representative cases
Before employing this new multiple charges model to the binding
of specific proteins, we apply it to three simple, but
Fig. 1 Graphical representation of the various parameters involved in
the definition of the model. The nano-wire is a cylinder of radius R and
length L, and is described by the parameters lTF (Thomas–Fermi length),
31 (nano-wire relative permittivity), m (charge carrier mobility) and n0 or
p0 (charge carrier density). The wire is coated with an oxide layer of
thickness DR with relative permittivity 32. Over the surface of the nano-
wire, at a distance li there are some charges Qi, which give a density sbi.
These charges are immersed in a buffer solution, described by lD (Debye
length) and its relative permittivity 33.
3636 | Nanoscale, 2011, 3, 3635–3640
representative, cases, in order to illustrate how the multiple
charges extension can give qualitatively different results
compared to a single charge model. In all three cases, the
modeled nano-wire is p-type doped and silicon based, with length
and diameter similar to those employed by the Lieber group
(Table 1S†),21 and a coverage corresponding to 5000 ‘‘proteins’’.
The employed Debye lengths (0–8 nm) are representative of
biologically relevant buffers.22
3.1.1 Single charge. Fig. 2b shows the change in conductance
sensitivity due to a single charge located between 1 to 5 nm from
the nano-wire surface (Fig. 2a), as a function of the Debye length
of the buffer solution. This corresponds to modeling a protein
as a single charge placed at its center of mass (COM), and the
1–5 nm is chosen to reflect the typical size of proteins (vide infra).
Fig. 2 shows that the signal is most sensitive to a change in Debye
length when the charge being sensed is closer to the surface. As
we discuss next, this has implications for proteins with uneven
charge distributions.
Fig. 2 Dependence of the conductance sensitivity (signal) of a Si p-type
doped nano-BioFET on the Debye length lD. Different biomolecule
models are reported, each constituted by one or more charges at constant
internal distance. The signal is evaluated at different distances D (in nm)
from the nano-wire surface. a) Single negative charge (m ¼ 1) and b) its
computed signal. c) Two differently charged charges (m ¼ 2, neutral
system) and d) their computed signal. e) Three differently charged
charges (m ¼ 3, system charge ¼ �1) and f) their predicted signal.
This journal is ª The Royal Society of Chemistry 2011
3.1.2 Two charges. Fig. 2d shows the change in conductance
sensitivity due to a neutral system, represented by two charges
with opposite sign and 1 nm apart (Fig. 2c). Based on the
conventional single charge interpretation of BioFET signals, one
would expect no signal change from the binding of a neutral
protein. However, a signal corresponding to a partial positive
charge is observed, since the positive charge of the neutral pair is
closer to the surface of the nano-wire and less screened by the
buffer solution than its counterpart. While the signal is weaker in
magnitude by a factor of 4 compared to a system with a single
charge (cf. the y axis of Fig. 2b and Fig. 2d), it would be suffi-
ciently strong to be measurable by state-of-the-art methods. We
note that the sensing of a system like Fig. 2c would induce
a signal only if all biomolecules were aligned and oriented in the
same way, while a random orientation would induce no signal.
3.1.3 Three charges. Fig. 2e shows a system consisting of two
negative and one positive charges (overall charge �1), set 1 nm
apart from each other. This system mimics a negatively charged
protein that possesses a positively charged region, which is
recognized by the bio-functionalized surface. With a single
charge model based interpretation, one would expect a change in
conductance sensitivity like the one presented in Fig. 2b. Instead
Fig. 2f shows a quite different signal caused by the different
distances of the three charges. Consider the D ¼ 1 nm curve. For
lD values from 0 to 0.5 nm the signal decreases with the Debye
length, as for a partial positive charge. After the value lD ¼ 0.5
nm the two negative charges are less and less shielded, causing
the signal to increase. When lD reaches�1.8 nm the conductance
sensitivity value is �0 (zero signal point ZSP with a relative
Debye length lD(ZSP)). Thus, it is evident that for Debye length
values between 0 and �1.8 nm, the predicted conductance
sensitivity signal has the opposite sign from the one expected
from a charge equal to the overall charge. Moreover, the sensing
of the system displayed in Fig. 2e represents a case when an
increase of the buffer Debye length would generate a counter-
intuitive decrease of the absolute value of the recorded signal.
For Debye length values larger than lD(ZSP), the buffer shielding
the two negative charges is less pronounced and the dominating
effect of the positive charge closest to the surface disappears. The
signal intensity and lD(ZSP) will be influenced by the dynamical
motion of the analyte, both internal motion and motion relative
to the nano-wire surface. To a first (harmonic) approximation,
the internal motion will not affect the average position of the
charges, leaving the signal unchanged. The effect of dynamical
motion relative to the nano-wire surface on the signal intensity
and lD(ZSP) for the system depicted in Fig. 2e is estimated in
Fig. 7S.† The figure shows that the ZSP persists even when the
system is tilted by 45�, though both the lD(ZSP) and the magni-
tude of the negative signal decreased.
3.1.4 Other cases. Results for other charge distributions are
presented as Supplementary Information, in order to further
elucidate the possible occurrence of a ZSP. Fig. 1S† shows the
occurrence of a ZSP for biomolecules constituted by 5 charges.
The two systems can be seen as representing a quite elongated
protein (Fig. 1Sa†) or a small protein containing a metal ion
(Fig. 1Sc†). In both cases, the uneven charge distribution creates
a ZSP. Fig. 2S† (three charges separated by different distances)
This journal is ª The Royal Society of Chemistry 2011
shows that lD(ZSP) depends primarily on the size of the consid-
ered system (Fig. 2Sb, d, f†) and secondarily by the overall
distance D of the molecule from the nano-wire surface
(Fig. 2Se†). Conversely, Fig. 3S† shows that lD(ZSP) is not
influenced by changing the conductive properties of the nano-
wire (i.e. varying lTF). Fig. 4S† shows that a ZSP also occurs for
a minimal system composed by two charges and overall charge
�1. This system is a simplified model of Fig. 2e. The occurrence
of a ZSP is independent of the sign of the overall charge; by
inverting the signs of the charges of the system of Fig. 2e, a ZSP
is still expected, with opposite sign of the signal. This is verified in
Fig. 5Sb.† The occurrence of a ZSP is connected to the relative
orientation of the biomolecule with respect to the nano-wire
surface. As shown in Fig. 6S,† when the system shown in Fig. 2e
approaches the surface from the negative side there is no ZSP.
Vide infra when discussing the N protein.
3.1.5 Ideal experiment. Fig. 3 presents the application of the
previous results to an idealized protein. Let us consider an ana-
lyte protein containing three ionized groups, one positive and
two negatives, and approximate it a) as a single charge, b) as
divided into two main parts, one positive and one negative, or c)
without approximations. The relative signals are clearly
different, with different values at long Debye lengths and those
relative to b) and c) showing a ZSP. Thus, it is shown that for
asymmetric charge distributions the multiple charges model is
necessary to correctly evaluate (i) the signal sign at short Debye
lengths, and (ii) the signal intensity at longer lengths. Only once
lD is larger than the dimensions of the analyte is the sign of the
signal as expected from the overall analyte charge. A state-of-
the-art experiment could be used to analyze the structure of the
analyte in terms of charge–surface distance by fine tuning the
buffer Debye length.
3.2 Real proteins
We now show the application of the multiple charges model to
the recognition of real proteins by BioFETs. The program
PROPKA23,24 is used to compute the charge distributions of
proteins of known structure. Given a protein structure,
PROPKA computes the pKa value of each ionizable amino acid.
Based on the computed pKa value, it is possible to determine the
protonation state of each ionizable amino acid based on a pH
value. See also eqn (S12).†
3.2.1 Streptavidin. First, we discuss the recognition of
Streptavidin by a biotinylated nano-BioFET. We will compare
the predicted signal dependence from the buffer Debye length
based on the multiple charges model with the results of the single
charge model16 and experimental data.18,25 The details of the
protein related parameters description are given as Supplemen-
tary Information.† The naturally occurring form of Streptavidin
is a homo-tetramer of interdigitated chains, i.e. four equivalent
chains in an alternating antiparallel arrangement (Fig. 8S†). The
computed charges and arrangement of the ionizable amino acids
at pH 7.4 are depicted in Fig. 4a. We simulate the recognition of
N ¼ 4727 proteins, each represented by m ¼ 104 charged groups,
with overall charge �8.49.
Nanoscale, 2011, 3, 3635–3640 | 3637
Fig. 3 An analyte with asymmetrical charge distribution, overall chargem¼�1, and COM–nano-wire surface distanceD¼ 2 nm, can be approximated
by a) its overall charge, b) the overall charge of its parts, and c) its single charges; d) reports the different computed conductance sensitivity signals.
The interdigitated chain structure of Streptavidin results in
even distributions of the otherwise un-evenly charged single
chain (vide infra). The result of this can be seen in Fig. 4b. The
multiple charges model predicted signal (red line) at different
Debye lengths for a p-type doped Si nano-BioFET (Table 1S†)
compares well with that of the single charge model (blue dots). In
this case (highly symmetric analyte), the multiple charges model
can be approximated by the single charge model.
Recently, Ishikawa et al.18 showed the signal obtained when
Streptavidin is adsorbed on the biotinylated surface of an indium
oxide (In2O3) based nano-BioFET. In2O3 is an n-type intrinsic
semiconductor, and a negative species approaching the nano-
wire surface should produce a negative signal. Instead, a positive
signal was recorded, which the authors attributed to positive
amine groups closer to the binding pocket. However, as we show
in Fig. 4, a change in signal sign is not predicted at any value of
Debye length, and our model suggests that there must be some
other reason for the observed sign of the conductance change.
One way of modifying the protein charge distributions is by
changing the pH of the simulated buffer solution. However, the
charge distribution remains even, given the interdigitated struc-
ture. Only by lowering the pH value under the protein isoelectric
point pI�526,27 (Fig. 10S†) is a positive signal expected. However
the buffer solution, though diluted, should have maintained the
pH around the value of 7.4.
Fig. 4 Dependence of the conductance sensitivity (signal) of a Si p-type do
(4 interdigitated chains, natural form) linking to a biotinylated surface. a) The
green. Superimposed, the position of the ionizable amino acids (m ¼ 104, sys
depending on their charge. Color code: red �1 charge, blue +1 charge, white
sponding color. The structure is aligned with the depicted axes. The nano-wire
negative direction of the x axis. b) The computed signal is shown as red contin
reported as blue dots.
3638 | Nanoscale, 2011, 3, 3635–3640
A plausible explanation could be that only a part of the
Streptavidin tetramer is sensed. While Streptavidin is highly
stable in its tetrameric form28 and the strong biotin affinity is
mainly due to interactions between two chains,29 the dimensions
of the Streptavidin tetramer (Fig. 8S†) are roughly the same as
the radius of the nano-wire employed by Ishikawa and co-
workers, ca. 5 nm. Thus, it is possible that the entire tetramer
does not fit on the nano-wire surface, and only a part of it is
sensed (roughly corresponding to e.g. a single chain), contrary to
what happens in the experiments of Stern et al. where the
employed nano-ribbons had a width of 50–150 nm.30 A single
chain structure of Streptavidin presents a more distinct charge
distribution and its sensing could induce a positive signal
(Fig. 11S†). Further experimental investigation (e.g. using nano-
wires such as those employed by Ishikawa and co-workers but
with different radii) could shed more light on this mechanism.31
3.2.2 Nucleocapsid protein. The same authors recently pub-
lished the results of another experiment where Nucleocapsid (N)
protein was recognized by a bio-functionalized In2O3 based
nano-BioFET.17 N protein has a computed overall charge of 6.82
at pH 7.4. Since In2O3 is an n-type semiconductor, a positive
charge approaching its surface should induce a positive signal.
Instead the recorded signal for the recognition of N protein was
negative.17 The authors suggest that this may be caused by
ped nano-BioFET on the Debye length lD for the Streptavidin protein
Streptavidin structure (in gray) with the position of the biotin molecules in
tem charge �8.49 as computed at pH 7.4) as spheres differently colored
neutral. Partial charges are reported with different shades of the corre-
surface is 2.3 nm distant from the protein COM (yellow sphere) along the
uous line. The data computed in ref. 16 with the single charge model are
This journal is ª The Royal Society of Chemistry 2011
negative regions of Nucleocapsid protein binding to the (posi-
tively charged) nano-wire surface (In2O3 pKa ¼ 8.7).32
The details of modeling the protein coverage and the bio-
functionalization layer are given as Supplementary
Information.† Fig. 5a reports the structure of N protein, with the
Fig. 5 Dependence of the conductance sensitivity (signal) of an In2O3 n-
type semiconducting nano-BioFET on the Debye length lD for N protein.
a) Structure of the N protein (in gray) with approximate dimensions.
Superimposed, the position of the ionizable amino acids (m ¼ 45, system
charge 6.82 as computed at pH 7.4) as differently colored spheres, as in
Fig. 4. The structure is aligned with the depicted axes. b) Computed signal
for different approaching directions. The direction of the cloning artifact
(�z) is not considered. Distances D of the protein COM (yellow sphere)
from the surface and number N of sensed proteins as reported in Table
3S.† c) The computed signal when the protein is adsorbed directly on the
nano-wire surface along the negative direction of the y axis.
This journal is ª The Royal Society of Chemistry 2011
computed charges of its ionizable amino acids superimposed as
per the pKa values computed by PROPKA at pH 7.4. Briefly, the
structure is composed by (i) a hairpin (located along the +y
direction), which is responsible for the recognition of RNA, and
is constituted mainly by positively charged groups, (ii) a cloning
artifact and expression tag along the�z direction, and (iii) a bulk
part, mainly constituted by negative charges, along the �y
direction.
Fig. 5b presents the computed signal when N protein is
recognized by a 6 nm thick bio-functionalization layer (see the
Supplementary Information†) over the surface of an In2O3 based
nano-wire (Table 2S†) for five different binding orientations. In
fact the experimentally employed bio-functionalization layer was
tailored to capture the RNA sensing fragment of N protein,33 but
it is not known if N protein would approach the capture agent
from the top or the side. As previously noted, different
approaching directions give different signals. Only when the
protein binds in the �y orientation is a (weak) negative signal
change possible for a buffer with Debye lengths less than ca. 2 nm
(red curve in Fig. 5b). If the protein binds directly to the nano-
wire surface, or can get close to it, the negative signal change is
significantly stronger (Fig. 5c), with a maximum for a buffer
Debye length of 1 nm.
However, it should be noted that in the experiments by Ishi-
kawa et al.17 the employed buffer corresponds to a Debye length
of around 7–8 nm, which is longer than that consistent with
a negative signal change according to Fig. 5. Our predicted signal
is always positive for lD values greater than 4–5 nm. As previ-
ously noted (vide supra), once the Debye length equals the ana-
lyte dimensions, the computed signal sign is as expected from the
overall charge. Not even the adsorption of the protein directly on
the surface of the nano-wire creates a negative signal at this
buffer dilution (Fig. 5c). As previously noted (vide supra)
the occurrence of a ZSP and its lD(ZSP) is mainly affected by the
charge distribution of the protein, and less by the distance to the
nano-wire surface.
4 Conclusions
In summary, we extend our screening model of surface charge
sensors in liquids to model the charge distributions of the analyte
proteins with multiple charges rather than a single charge
(Fig. 3). We use this model to show that counter-intuitive
changes in the signal (e.g. a positive signal change due to a net
positive protein binding to a p-type semi-conductor) can occur
for certain combinations of (prototypical) charge distributions
and Debye lengths (Fig. 2).
The new method is applied to interpret previously published
experimental data on Streptavidin and Nucleocapsid protein. In
the case of Streptavidin we show that modeling the charge
distributions as a single charge is a good approximation for any
choice of Debye length (Fig. 4) and that the counter-intuitive
signal change due to Streptavidin binding observed by Ishikawa
et al.18 is unlikely to be caused by charges closer to the surface,
unlike their suggestion. In the case of Nucleocapsid protein17 we
show that the multiple charges model predicts the possibility of
a negative signal (when a positive one would be expected based
on the overall protein charge). However, such negative signals
are expected for buffer Debye lengths shorter than that reported
Nanoscale, 2011, 3, 3635–3640 | 3639
in the experiment, even if the protein is directly adsorbed at the
nano-wire surface.
We note that the approximations used in treating the nano-
wire response may limit its accuracy when applied to very thin
(R < 5 nm) nano-wires in general and to In2O3 nano-wires in
particular, because the effect of electron accumulation at the
surface34 is neglected.
We hope our new method will help in the design and inter-
pretation of experiments that address more subtle aspects of
analyte binding, such as the effect of protein orientation35,36
(Fig. 2d and f and Fig. 6S†) or conformational changes upon
binding. The software package (BioFET-SIM) written to predict
the conductance sensitivity is open source (distributed under the
GNU GPL) and can be obtained by contacting the authors. A
web interface can be found at the address http://propka.ki.ku.dk/
biofet-sim.
Acknowledgements
The authors acknowledge Nathalie Rieben and Yi-Chi Liu for
fruitful discussions about the results. Funding has been provided
by the Danish Research Council for Technology and Production
Sciences (FTP), the Danish Natural Science Research Council
(FNU), and by UNIK Synthetic Biology, funded by the Danish
Ministry for Science, Technology and Innovation.
Notes and References
1 M. J. Sch€oning and A. Poghossian, Electroanalysis, 2006, 18, 1893–1900.
2 M.W. Shinwari, M. J. Deen and D. Landheer,Microelectron. Reliab.,2007, 47, 2025–2057.
3 D. Grieshaber, R. MacKenzie, J. V€or€os and E. Reimhult, Sensors,2008, 8, 1400–1458.
4 C.-S. Lee, S. K. Kim and M. Kim, Sensors, 2009, 9, 7111–7131.5 S. Roy and Z. Gao, Nano Today, 2009, 4, 318–334.6 J. N. Israelachvili, Intermolecular and surface forces, Academic Press,London; San Diego, 2nd edn, 1991.
7 J.-i. Hahm and C. M. Lieber, Nano Lett., 2004, 4, 51–54.8 P. R. Nair and M. A. Alam, Appl. Phys. Lett., 2006, 88, 233120.9 P. Nair and M. Alam, IEEE Trans. Electron Devices, 2007, 54, 3400–3408.
10 P. R. Nair and M. A. Alam, Nano Lett., 2008, 8, 1281–1285.11 C. Heitzinger and G. Klimeck, J. Comput. Electron., 2007, 6, 387–390.
3640 | Nanoscale, 2011, 3, 3635–3640
12 C. Heitzinger, R. Kennell, G. Klimeck, N. Mauser, M. McLennanand C. Ringhofer, J. Phys.: Conf. Ser., 2008, 107, 012004.
13 C. Ringhofer and C. Heitzinger, ECS Trans., 2008, 14, 11–19.14 S. Birner, C. Uhl, M. Bayer and P. Vogl, J. Phys.: Conf. Ser., 2008,
107, 012002.15 Y. Liu and R. W. Dutton, J. Appl. Phys., 2009, 106, 014701.16 L. De Vico,M. H. Sørensen, L. Iversen, D.M. Rogers, B. S. Sørensen,
M. Brandbyge, J. Nyg�ard, K. L. Martinez and J. H. Jensen,Nanoscale, 2011, 3, 706–717.
17 F. N. Ishikawa, H.-K. Chang, M. Curreli, H.-I. Liao, C. A. Olson,P.-C. Chen, R. Zhang, R. W. Roberts, R. Sun, R. J. Cote,M. E. Thompson and C. Zhou, ACS Nano, 2009, 3, 1219–1224.
18 F. N. Ishikawa, M. Curreli, H.-K. Chang, P.-C. Chen, R. Zhang,R. J. Cote, M. E. Thompson and C. Zhou, ACS Nano, 2009, 3,3969–3976.
19 M. H. Sørensen, N. A. Mortensen and M. Brandbyge, Appl. Phys.Lett., 2007, 91, 102105.
20 For an n-type semiconductor it is necessary to remove the factor�1 ineqn (1), (S3) and (S5),† and use the appropriate value for the chargecarrier density (n0 instead of p0) and mobility where needed.
21 Y. Cui, Z. Zhong, D. Wang, W. U. Wang and C. M. Lieber, NanoLett., 2003, 3, 149–152.
22 Protein function is generally dependent on a proper solution ionicstrength, preferably in the physiological range of �150 mM.
23 H. Li, A. D. Robertson and J. H. Jensen, Proteins: Struct., Funct.,Bioinf., 2005, 61, 704–721.
24 D. C. Bas, D. M. Rogers and J. H. Jensen, Proteins: Struct., Funct.,Bioinf., 2008, 73, 765–783.
25 E. Stern, R. Wagner, F. J. Sigworth, R. Breaker, T. M. Fahmy andM. A. Reed, Nano Lett., 2007, 7, 3405–3409.
26 N. M. Green, in Avidin-Biotin Technology, ed. M. Wilchek and E. A.Bayer, Academic Press, 1990, vol. 184, pp. 51–67.
27 L. Chaiet and F. J. Wolf, Arch. Biochem. Biophys., 1964, 106, 1–5.28 M. Gonz�alez, C. E. Argarana and G. D. Fidelio, Biomol. Eng., 1999,
16, 67–72.29 T. Sano and C. R. Cantor, Proc. Natl. Acad. Sci. U. S. A., 1995, 92,
3180–3184.30 E. Stern, J. F. Klemic, D. A. Routenberg, P. N. Wyrembak,
D. B. Turner-Evans, A. D. Hamilton, D. A. LaVan, T. M. Fahmyand M. A. Reed, Nature, 2007, 445, 519–522.
31 We are also currently considering a more complex model that takesinto account not only the vertical distance of a charge from thenano-wire surface, but also its distance from the surface edge.
32 M. Kosmulski, J. Colloid Interface Sci., 2001, 238, 225–227.33 X. Qi, T. Xia and R. W. Roberts, Biochemistry, 2010, 49, 5782–5789.34 P. D. C. King, T. D. Veal, D. J. Payne, A. Bourlange, R. G. Egdell
and C. F. McConville, Phys. Rev. Lett., 2008, 101, 116808.35 C. Heitzinger, N. J. Mauser, C. Ringhofer, Y. Liu and R. W. Dutton,
Proc. Simulation of Semiconductor Processes and Devices (SISPAD2009), San Diego, CA, USA, 2009, pp. 86–90.
36 C. Heitzinger, N. J. Mauser and C. Ringhofer, SIAM J. Appl. Math.,2010, 70, 1634–1654.
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