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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

http://dx.doi.org/10.1039/c1nr10316d





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.


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)


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


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.


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.

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