Analytical Model To Describe the Effect of Polyethylene Glycol on Ionic

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Analytical model to describe the effect of poly-ethylene glycol on ionic screening of analyte charges in transistor-based immunosensing Natalie Haustein, Oscar Gutierrez-Sanz, and Alexey Tarasov ACS Sens., Just Accepted Manuscript • DOI: 10.1021/acssensors.8b01515 • Publication Date (Web): 06 Mar 2019 Downloaded from http://pubs.acs.org on March 7, 2019

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Analytical model to describe the effect of poly-ethylene glycol on ionic screening of analyte charges in transistor-based immunosensing Natalie Haustein, Óscar Gutiérrez-Sanz, Alexey Tarasov* BioMed X Innovation Center, 69120 Heidelberg, Germany E-mail: [email protected], [email protected]

Abstract Recently, the co-immobilization of poly-ethylene glycol has improved sensor responses of transistorbased immunosensing by approximately three times. However, there is currently no analytical model available to explain this empirical effect. The key parameters thought to affect the potential are the receptor density, the capacitance, the analyte charge and the dissociation constant. Based on our experimental data, only the analyte charge can account for the signal enhancement. To capture the effect of PEG on the analyte charge, we introduce a pre-factor, the detectable charge qdet, which represents the portion of analyte charges effectively detected by the sensor. This parameter can quantitatively describe the PEG-induced signal enhancement and can be used to recommend the choice of PEG size for immunoFETs. Additionally, we include the competition between electrolyte ions and the analyte for binding to the recognition molecule to more accurately describe the concentrationdependent sensor responses than the traditional Langmuir binding model. Debye screening length, field effect transistor, immunosensing, Donnan potential, competitive binding Ion-sensitive field-effect transistors (ISFETs) have proven to be a reliable sensing technique for small and highly charged species such as pH and metal ions.1,2 However, the detection of larger and less densely charged molecules such as proteins still poses a challenge. When molecules bind to the sensor surface, their net charge changes the surface potential, which modulates the ISFET channel current via the field effect. Also, the supporting electrolyte ions accumulate on the sensor surface resulting in an electrical double layer that screens the analyte charges. This ionic screening becomes more pronounced with increasing number of ions, expressed by the so-called Debye screening length. Especially in physiological solutions with high ionic strength such as buffers and undiluted donor samples (serum, whole blood, sweat, etc.) the Debye screening length decreases to less than 1 nm. Proteins are several times larger than that and, as a result, most of their charge will be screened, leading to only small potential shifts. Additionally, the specific detection of proteins requires recognition molecules ranging from aptamers

3–7

and nanobodies

8

to antibodies

9,10

and their

fragments.11,12 For such direct immunoassays, the recognition molecule is typically immobilized to the ACS Paragon Plus Environment

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sensor surface and then exposed to the analyte solution, making the distance between the analyte and the sensor surface even longer. Several recent papers explored different strategies to overcome the Debye screening.3,8,11–16 A particularly promising approach is the co-immobilization of Poly(ethylene glycol) (PEG) together with recognition molecules, because it allows for analyte detection at physiological ionic strength without the need for washing or desalting steps. Several analytes have been successfully detected using this approach including thyroid-stimulating hormone (TSH) green-fluorescent protein (GFP)

8

11,12,

and prostate-specific antigen (PSA).3 Interestingly, in all cases

described so far, the usage of PEG led to a three-fold signal increase compared to a control surface without PEG. PEG is thought to locally decrease the effect of Debye screening, possibly by reducing the relative permittivity compared to water.3,14 However, to the best of our knowledge there is currently no analytical model to quantify the effect of PEG in immunosensing and to relate this effect to the signal increase expected for a certain analyte. Here, we used the systematic experimental study of Gutiérrez-Sanz and co-workers on immunosensing of TSH via an Anti-TSH F(ab’)2 fragment tethered to SAMs with and without PEG as a basis for developing analytical models to describe the potential shifts as a function of analyte concentration.11 Existing Langmuir-type analytical models include the receptor density, the interfacial capacitance, the analyte charge and the dissociation constant as main parameters affecting potential shifts. By directly measuring most of these parameters using different techniques, we found that the analyte charge is most likely the main factor determining signal enhancement in presence of PEG. To model the effect of PEG on the analyte charge, we assume that the surface layer comprised of the recognition molecule and PEG can be described by the Donnan potential theory. Based on this theory, it was described that the potential inside a surface layer may become nearly constant due to immobilized charges 17, which would result in much weaker Debye screening when PEG is present, or, in other words, a higher effective analyte charge. Mathematically, this can be expressed as a pre-factor of the analyte charge, called here the detectable charge qdet, which is a function of the analyte size, the position of the analyte with respect to the sensor surface, the ionic strength and the thickness of surface layer. We calculate qdet for experimental conditions provided by recent studies of the effect of PEG on the immunosensing of TSH

11,12,

GFP

8

and PSA

3

in different buffers. In each case, the increased detectable charge on

sensors with PEG agreed with the about three-fold higher potential shifts in the FET measurements. Based on this model, we recommend an appropriate PEG size for maximum response, based on the properties of the analyte and the recognition molecule of choice. Finally, we propose an extension of the conventional Langmuir-type model that also includes the competitive binding of electrolyte ions and the analyte. With this extension, the model more accurately describes the concentrationdependent response reported previously.

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Results and Discussion I.

Current model and critical parameters for sensor response

PEG has been experimentally shown to strongly increase the sensor response upon binding of protein analytes. In order to understand how PEG enhances the sensor response, critical parameters that affect the surface potential have to be identified. We chose an analytical approach to search for those critical parameters. The analytical model that represents the current understanding of how the surface potential changes with the concentration of analyte is based on Langmuir binding.18 This model suggests that an analyte with charge q and bulk concentration cAnalyte is bound by a recognition molecule of surface density NR with a dissociation constant KD. The surface charge provided by these analytes results in the surface potential drop Ψ over the interfacial capacitance C: 𝛹=

𝑞 𝑁𝑅

𝑐𝐴𝑛𝑎𝑙𝑦𝑡𝑒

(1)

𝐶 𝑐𝐴𝑛𝑎𝑙𝑦𝑡𝑒 + 𝐾𝐷

In principle, all four parameters present in Eq. 1 (i.e. q, C, NR and KD) can be influenced by PEG, leading to higher potential shifts. To assess their relative contributions to the experimentally observed threefold potential increase with PEG, we decided to measure most of these parameters using different techniques. We choose TSH as a model antigen which is recognized by anti-TSH F(ab’)2 coupled to either a self-assembled monolayer (SAM) of linker molecules only (COOH-EG8-thiol) or to a mixed SAM of these linker molecules and PEG (mPEG-thiol, 10 kDa) in a 1:20 molar ratio. All measurements were performed at room temperature to match the FET measurements conducted by Gutiérrez-Sanz and co-workers. The capacitance was measured by electrochemical impedance spectroscopy on gold electrodes with the different SAMs and with immobilized F(ab’)2 fragment in 10 mM and 150 mM. The capacitance was calculated, assuming a RC equivalent circuit, at the frequency at which maximum phase shift occurs19 (see Table 1). For the measured impedance spectra and the detailed calculation of capacitance please refer to the SI. The measured capacitances were in the range of 12 to 14 µF/cm2 agreeing with values expected for electrolyte-gated systems.13,19 Although the capacitance was thought to be the reason for the increased signals, e.g. due to a decrease of dielectric constant

3,14,

the addition of PEG has only

little effect on the interfacial capacitance at high ionic strength. These marginal differences cannot account for the observed threefold signal increase or for the expected differences between low and high ionic strength (see Figure S 2A). The surface density of recognition molecules was calculated from the quartz crystal microbalance measurements done by Gutiérrez-Sanz and co-workers and found to be 2.1×1016 m-2 on SAM without PEG and 2.3×1016 m-2 on SAM with PEG, which corresponds to a mere 10 % difference in NR, far away from the expected three-fold signal increase (see Figure S 2B). The dissociation constant KD for the TSH-antibody interaction used here is 0.19 nM at room temperature ACS Paragon Plus Environment

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(provided by the manufacturer).11 All three critical parameters were measured on gold surfaces to match the gold extended-gate FET measurements conducted by Gutiérrez-Sanz and co-workers. However, we note that the results may differ on when other gate materials like in carbon-based 3,8,12 or silicon-based14 FETs are used instead. From these measurements, we can exclude three out of four parameters in Eq. 1 due to their insignificant contributions to the overall signal change, leaving the analyte charge q as the only parameter that can still be substantially altered by PEG. II.

Quantifying the portion of net charge effectively detected by the sensor

The net charge of a protein depends on its structure and the pH of the electrolyte it is dissolved in. However, it is expected that the charge of the analyte which can be detected by an FET also depends on the ionic strength of the electrolyte represented by the Debye screening length.20–23 The Debye screening length λD (or 1/Κ) is calculated by: 𝜆𝐷 = 𝜅 ―1 =

𝜀0𝜀𝑟𝑘𝐵𝑇

(2)

2𝑁𝐴𝑒2𝐼

with the relative permittivity εr, the ionic strength I, the temperature T, and the physical constants vacuum permittivity ε0, Boltzmann constant kB, Avogadro constant NA and elementary charge e. The potential distribution at a charged surface in contact with a liquid electrolyte predicts an exponential decay of the surface potential with increasing distance from the electrode x (Eq. 3). Equation 3 is the solution of the linearized Poisson-Boltzmann equation (valid for potentials less than kBT 𝑒) with the decay constant given by the Debye screening length λD = κ-1 (see Figure 1A and B): 𝛹 = 𝛹0 𝑒 ―𝜅𝑥

(3)

Applied to the work of Gutierrez-Sanz et al., this would mean that the signals due to TSH binding will be strongly suppressed because the TSH binding to the capture antibody fragment is assumed to take place approximately 7.8 nm away from the surface. For example, at 150 mM ionic strength only 0.006 % of initial surface potential remains at this distance and at 10 mM only 8 %. Whereas Eq. 3 considers an electrode in direct contact with an electrolyte, surface layers separate the liquid electrolyte from the electrode surface. Pronounced surface layers have been recently shown to increase the effective Debye length.15 Ohshima proposed a model for potential distribution across surfaces based on the Donnan theory for particles where a surface layer separates the solid particle core and the electrolyte (see Figure 1C).17 In this picture, the potential at the particle core surface (the Donnan potential ΨDON) stays approximately constant within the surface layer due to ions that can penetrate and then are

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immobilized inside (cIons,DON). The potential distribution follows a sigmoidal decay, again influenced by the Debye screening length 1/κ, inside (eq. 5) and outside (eq. 6) of the surface layer of thickness d

(

𝛹𝑖𝑛(𝑥) = 𝛹𝐷𝑂𝑁 1 ―

𝑒𝜅𝑥 + 𝑒 ―𝜅(𝑥 + 2𝑑) 2

), for –d < x < 0

(4)

1

𝛹𝑜𝑢𝑡(𝑥) = 2𝛹𝐷𝑂𝑁(1 ― 𝑒 ―2𝜅𝑑)𝑒 ―𝜅𝑑, for x > 0

(5)

As can be seen from Figure 1D, the Debye screening starts to play a role further away from the electrode surface, namely close to the interface to the electrolyte. This would imply that if analyte binds predominantly within the surface layer then a significant portion of its charge may be detectable. The 10 kDa-PEG used during the surface modification step forms such a surface layer that surrounds the F(ab’)2 fragment and the analyte. A combination of measurements, including liquid atomic force microscopy imaging and force measurements, showed that the PEG in the mixed SAM forms a brushlike layer that dominates the behavior of the overall surface (see SI section V. for further information).24 Therefore, we use the Donnan potential picture (Equations 4 and 5) rather than the regular surface potential picture (Equation 3) as we believe it to better represent the modified sensors investigated in this study. This model is used as a basis to quantify the amount of analyte charges effectively detected by the sensor. We assume the analyte charge to be comprised of the net total charge n0 and the portion of charge detectable. This detectable charge qdet we define to be a value between 1 (all charges are detectable) and 0 (no portion of charges is detectable) depending on the where the analyte binds with respect to the surface layer x0. Qualitatively, we assume that the most charge is detectable if the analyte binds directly to the metal inside the surface layer and less amount is detectable if the binding occurs further away from the sensor surface. Since proteins have a smaller charge-to-size ratio than ions and cannot be viewed as point charges, we also consider the size of the analyte as a critical factor. More of the distributed charges on the side of the analyte that is closer to the electrode will be detectable than on the side further away from the electrode (Figure 2A). To represent these assumptions quantitatively and correlate them to the Donnan model, we define qdet to be the integral of the distance-dependent potential decay over the position and the analyte size (Figure 2B). We reference this value to the analyte size dAnalyte resulting in a dimensionless number between 0 and 1. If all distributed analyte charges are inside the surface layer (x0 + dAnalyte ≤0): 1

𝑥 + 𝑑𝐴𝑛𝑎𝑙𝑦𝑡𝑒

𝑞𝑑𝑒𝑡,𝐼 = 𝑑𝐴𝑛𝑎𝑙𝑦𝑡𝑒 ∫𝑥0 0

(1 ―

𝑒𝜅𝑥 + 𝑒 ―𝜅(𝑥 + 2𝑑) 2

) ∙ 𝑑𝑥

If all distributed analyte charges are outside the surface layer (x0 ≥ 0):

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(6).

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1

𝑥 + 𝑑𝐴𝑛𝑎𝑙𝑦𝑡𝑒1 2 0

(1 ― 𝑒 ―2𝜅𝑑)𝑒 ―𝜅𝑑 ∙ 𝑑𝑥

𝑞𝑑𝑒𝑡,𝐼𝐼 = 𝑑𝐴𝑛𝑎𝑙𝑦𝑡𝑒 ∫𝑥0

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(7).

And if the distributed analyte charges are partly inside and outside of the surface layer (x0 < 0 and x0 + dAnalyte > 0): 1

0

(

𝑞𝑑𝑒𝑡,𝐼𝐼𝐼 = 𝑑𝐴𝑛𝑎𝑙𝑦𝑡𝑒 ∫𝑥 1 ―

𝑒𝜅𝑥 + 𝑒 ―𝜅(𝑥 + 2𝑑)

0

2

) ∙ 𝑑𝑥 + ∫

𝑥0 + 𝑑𝐴𝑛𝑎𝑙𝑦𝑡𝑒1 2 0

(1 ― 𝑒 ―2𝜅𝑑)𝑒 ―𝜅𝑑 ∙ 𝑑𝑥

(8).

These equations describe the detectable charge qdet as a function of: analyte size dAnalyte, ionic strength (represented by κ), position of the analyte x0 and the surface layer thickness d. As qualitatively explained before, qdet is expected to decrease with distance of analyte with respect to the sensor surface and to be higher for sensors with PEG compared to those without. To prove this behavior, we calculated qdet for various possible positions for an exemplary analyte on a surface with a short surface layer of 8.6 nm, corresponding to F(ab’)2 fragment on a SAM without PEG (Figure 2C, red line), and a longer surface layer of 10.8 nm, corresponding to F(ab’)2 fragment on mixed SAM with PEG (Figure 2C, blue line). As expected, qdet drops from 1 towards 0 following a sigmoidal shape and is higher in the case of SAM with PEG than without PEG. At a certain distance, qdet on SAM with PEG becomes three times higher than on SAM without PEG (Figure 2C, arrow). In this example, that distance is 7.8 nm away from the sensor surface, corresponding to roughly 1 nm shorter than the combined length of linker and recognition molecule. After validating the qualitative behavior, we apply this model to the measurements conducted by Gao3, Gutierrez-Sanz11, Filipiak8, Andoy12, and their co-workers. In each publication the authors show the signal enhancing properties of PEG in solution of varying ionic strength ranging from 1 mM to 150 mM. Table 2 shows the recognition molecule, analyte and the ionic strength of buffer that were used in these publications. The reported maximal potential shifts (at the highest analyte concentration measured) for the sensors without and with PEG are noted and the ratio between them calculated. The required parameters to calculate qdet were deducted from the layout of the sensor. As a simplification, the properties and geometry of the transducer are neglected, and the analyte charges assumed to be evenly distributed. The sizes of proteins were calculated from their crystal structures using the PyMOL script “draw protein dimensions” by Pablo Guardado Calvo 25 (see SI for a complete list). The surface layer thickness d was assumed to be the combined length of linker and recognition molecules, for SAMs without PEG, and assumed to be the length of 10 kDa PEG molecules, for SAMs with PEG. We measured the thickness of a 10 kDa PEG surface layer using multi-parametric surface plasmon resonance as described elsewhere.26–28 The measured thickness of 10.8 nm agrees with expected values for 10 kDa PEG-thiol on gold (see SI for more details).28

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Because the position of the analyte with respect to the sensor surface was not known in these cases, we calculated qdet for every possible position as shown exemplary in the previous section. At a certain distance of analyte binding, the qdet ratio takes the same value as the ratio between potential shifts with to without PEG. For all analytes this distance is about 1 ± 0.2 nm shorter than the combined length of linker and recognition molecule. That indicates that the analytes bind not exactly on top of the recognition molecule but inside the surface layer, which can be explained be the three-dimensional structure of the binding site and the random orientation of the recognition molecule. In the case of GFP binding to an anti-GFP nanobody, it was observed that GFP binds to the side of the nanobody, agreeing with the interpretation of our results.29 The detectable charge that was calculated at these positions is noted in Table 2. The detectable charge model can help to design better sensors for immunodetection based on the analyte of interest and the available recognition molecule. In Figure 3 we calculated the detectable charge for three different hypothetical analytes from small (1 nm) over medium sized (5 nm) to big (10 nm) analytes, corresponding roughly to typical sizes of metabolites, hormones and antibodies. A selection of recognition elements is chosen from aptamers over nanobodies, F(ab’)2 fragments and whole IgG antibodies. The larger the analyte and the recognition molecule, the longer the PEG should be to ensure a reasonable amount of detectable charge. As a rough estimate we recommend that the PEG used for a sensor should be at least as long as the combined length of linker, recognition element, and analyte to yield more than 50 % detectable charge. III.

Competitive binding for analyte detection from high ionic strength electrolytes

We showed in the previous section that the differences in sensor response with and without PEG on the surface can be explained by the differences in detectable analyte charge. As mentioned above, a common model for concentration-dependent signal changes relies on the Langmuir binding model for one analyte binding to a recognition molecule. Figure 4A shows a schematic representation of the sensor layout and the interaction of molecules represented in the Langmuir model. The analyte of bulk concentration cAnalyte has a total net charge n0 which, combined with the detectable charge qdet, makes up the analyte charge. The analyte is bound by the recognition molecule of surface density NR with a dissociation constant KD. Other effects from the electrolyte are not considered. In Figure 4B, we compare the calibration curve measurements for TSH binding to F(ab’)2 fragment as recognition molecule on sensor without and with PEG in 10 and 150 mM ionic strength buffer as reported by Gutiérrez-Sanz and co-workers (points) to simulated data based on the Langmuir binding model (lines).11 We used the values calculated for qdet, the measured values for NR, capacitance CDL, and KD according to equation 1. Compared to the sensor response it is evident that the Langmuir model does not accurately represent the actual calibration curve measurements. The simulated potential ACS Paragon Plus Environment

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shifts for the sensor with PEG (blue) are as expected overall higher than the ones without (red). However, the differences in ionic strength are not represented by the Langmuir-based model. The Langmuir-based model also fails to account for the wider dynamic range commonly observed for transistor-based immunosensors. A wide dynamic range has been attributed before to differences in dissociation constant caused by the random adsorption of the recognition molecule to the surface.23 Although we acknowledge the possibility of differences due to random immobilization of the F(ab’)2 fragment, we propose an alternative model based on competitive binding of analyte and buffer ions to the surface. The Langmuir model only accounts for potential shifts provided by the analyte with a certain (high) affinity. However, the analyte is only present in a very small concentration compared to the high number of ions in physiological solutions. These ions will also interact with the surface, although with a lower affinity. Figure 4C shows a simplified scheme of the adsorption we expect to occur during sensing: The analyte (TSH) at a bulk concentration cAnalyte and with total net charge n0 and detectable charge qdet is bound by the recognition molecule (F(ab’)2 fragment) of surface density NR with the dissociation constant KD. Ions of bulk concentration cIons from the electrolyte weakly adsorb to the same recognition molecules with dissociation constant K1 and to the unoccupied surface groups of density NS with dissociation constant K2. The ions adsorbed to the unoccupied surface groups will follow a Poisson-Boltzmann distribution 30, whereas the ions adsorbed to the recognition molecules (cIons,DON) are described by the Donnan distribution31.

𝛹=

𝑒𝑁𝑅 𝐶

𝐾1𝑞𝑑𝑒𝑡𝑛0𝑐𝐴𝑛𝑎𝑙𝑦𝑡𝑒 + 𝐾𝐷 𝑐𝐼𝑜𝑛𝑠, 𝐷𝑜𝑛

∗ 𝐾1 𝑐𝐴𝑛𝑎𝑙𝑦𝑡𝑒 + 𝐾1𝐾𝐷 + 𝐾𝐷 𝑐𝐼𝑜𝑛𝑠, 𝐷𝑜𝑛 +

𝑒𝑁𝑆 𝐶

∗

(

𝑒𝛹

𝑐𝐼𝑜𝑛𝑠𝑒𝑥𝑝 ― 𝑘𝑇

(

𝑐𝐼𝑜𝑛𝑠𝑒𝑥𝑝 ―

𝑒𝛹 𝑘𝑇

)

)+𝐾

(9) 2

According to Bergveld, ions immobilized in the surface layer cIons,DON are replaced by the analyte 31: 𝑐𝐼𝑜𝑛𝑠, 𝐷𝑜𝑛 =

1 2

4𝑐2𝐼𝑜𝑛𝑠 + 𝑛0𝑞𝑑𝑒𝑡𝑐2𝐴𝑛𝑎𝑙𝑦𝑡𝑒 ― 𝑛0𝑞𝑑𝑒𝑡𝑐𝐴𝑛𝑎𝑙𝑦𝑡𝑒

(10)

The potential shift measured is the difference between the potential for the respective analyte concentration and the potential before analyte introduction where only ions are present ΔΨ = Ψ(cAnalyte) - Ψ(0). Where applicable, we used the same values as in the Langmuir-based model for simulation. The dissociation constants K1 and K2 were assumed to be 0.1 mM representing weak interaction and NS is assumed to be 10 % of the total amount of surface groups. In the SI, we simulate how the changes of these parameters may affect the sensor response. In short, the competitive binding model predicts a pronounced effect if KD and K1, i.e. the interaction with the recognition molecule, are modulated by the addition of PEG. A decrease of affinity of the analyte to the recognition molecule (lower KD) would lower the limit of detection. An increase of affinity of ions to the recognition molecule (higher K1) would also lower the limit of detection and additionally ACS Paragon Plus Environment

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increase the maximum potential shift. The adsorption of ions (represented by K2) to unoccupied surface groups was found to have only marginal effect on the sensor response and can be omitted when the surface is assumed to be saturated by recognition molecule. However, if the recognition molecules are purposefully immobilized at a low surface density, e.g. to reduce mass transport limitation, then this unspecific ion interaction may have a pronounced effect and should be considered. The simulated calibration curves for all surfaces are shown in Figure 4D (lines). Compared to the measured sensor response shown as points, this competitive model represents the actual measurements much better than the Langmuir-based model (Figure 4B lines). Unlike the Langmuir model, the competitive model accurately predicts that the potential shifts at low ionic strength are higher than at high ionic strength. In both, the actual FET measurements and the simulated calibration curve based on competitive binding, no saturation at high TSH concentration (above 10 nM) is achieved as was incorrectly predicted by the Langmuir based model. However, we still see discrepancies between modelled and measured data in the low concentration range, especially at low ionic strength when PEG is present (Figure 4D, light blue). This may be caused by the random orientation of the F(ab’)2 fragments by either increasing locally the detectable charge when TSH is bound closer to the sensor surface than expected for oriented fragments or by differences in KD as discussed before.23 We conclude that the background signal from the ion adsorption should not be ignored, as their concentration in physiological solution is orders of magnitude higher than the physiological concentrations of analyte. Although we were able to measure or calculate most of the parameters used in the model, some parameters, such as the dissociation constants rely on either data provided by the manufacturer (KD) or are estimated (K1, K2). The use of PEG may have an additional effect on these parameters that has not yet been investigated experimentally.

Materials and Methods Chemicals Ethanol, hydrogen peroxide, ammonia solution 25 %, bovine serum albumin (BSA) were purchased from Carl Roth GmbH + Co. KG. MES hydrate, 1-Ethyl-3-(3-dimethylaminopropyl) carbodiimide hydrochloride (EDC-HCl), N-hydroxysuccinimide (NHS) were purchased from Sigma-Aldrich Co. LLC. 10 kDa mPEG-thiol (PEG) was purchased from Creative PEGWorks and COOH-EG8-thiol (linker) was purchased from Celares GmbH. Both thiols were stored at -20 °C under inert conditions and prepared fresh for each experiment to ensure stability of the thiol-group. Electrochemical impedance measurements

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Screen-printed electrodes with gold working electrode, platinum counter electrode and silver reference electrode were purchased from Deutsche METROHM GmbH & Co KG. The screen-printed electrodes were rinsed with ethanol and water and dried with nitrogen. They were incubated in either 40 µM linker in 50 mM MES pH 7 (for SAM without PEG) or in a mix of 2 µM PEG and 40 µM linker in 50 mM MES pH 7 (for SAM with PEG) for 60 minutes. The sensors were rinsed with 50 mM MES pH 5.6 and immersed in 400 mg/mL EDC and 600 µg/mL NHS in 50 mM MES pH 5.6 for 20 minutes. Subsequently the sensors were incubated with 250 µg/mL Anti-TSH F(ab’)2 fragment in 50 mM MES pH 5.6 for 90 minutes. The surfaces were blocked with 60 mg/mL BSA in 50 mM MES pH 7 for 20 minutes. The sensors were washed with 50 mM MES pH 7 and mounted in the boxed connector for screen printed electrodes (DropSens) and connected to a µAUTOLABIII/FRA2 and PGSTAT204 from Metrohm Autolab B.V. (Metrohm AG). The samples were incubated in 10 or 150 mM MES pH 7 for 15 minutes prior to measurement. Electrochemical impedance spectroscopy measurements were performed by applying a 10-mV sinusoidal AC potential to the working electrode at frequencies from 100 kHz to 100 mHz (10 per decade) superimposed at 0 V against the reference electrode. Multiparametric-SPR measurements Gold covered sensor slides (BioNavis Ltd.) were cleaned in a 5:1:1 mixture of DI water, hydrogen peroxide and 25 % ammonia solution at 80 °C for 15 minutes, rinsed with DI water and dried with nitrogen. The gold slides were incubated for 60 minutes in either 40 µM of linker or 2 µM of PEG in 50 mM MES pH 7, rinsed in DI water and dried with nitrogen. The slides were mounted in the BioNavis SPR Navi 220A and consecutively exposed to 50 mM MES pH 7 for 5.5 min and 10 mg/mL BSA for 3.5 min at a flow rate of 40 µL/min in three successions. AFM measurements AFM-grade gold-covered glass slides (Ted Pella, Inc.) were plasma cleaned for 10 minutes and either measured directly (plain gold) or incubated for 60 minutes in either 40 µM of linker or 2 µM of PEG or a mix thereof in 50 mM MES pH 7 and subsequently washed in this buffer. Liquid AFM contact mode imaging (at 30 pN and 1 nN) and force measurements (at 200 pN) in buffer were performed with a JPK NanoWizard® 4 (Bruker Nano GmbH) using rectangular-shaped Si3N4 AFM-cantilevers (Biolever, Olympus/OBL) with V-shaped tip (nominal spring constant 6 pN/nm). Calculation of protein dimensions The dimensions of the analytes TSH, GFP and PSA, and the dimensions of F(ab’)2 fragment, nanobody and aptamer were calculated using the PyMOL “draw protein dimensions” script of Pablo Guardado Calvo 25. For GFP (1EMA) and PSA (1GVZ) their Protein Data Bank crystal structures were used, for the remaining proteins no crystal structures were available and instead molecular weight matched protein ACS Paragon Plus Environment

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structures from the same type and family were used. The lengths of the linkers were estimated from their chemical structure. For a full list of dimensions used in this study, please refer to SI section IV.

Conclusion We used a combination of multiple experimental techniques and analytical modelling to investigate how PEG increases the sensor response by more than three times in immuno-FETs. Among the relevant parameters that can be potentially influenced by PEG, we could exclude the surface density of recognition molecules and the interfacial capacitance due to insignificant differences between sensors with and without PEG. The remaining parameter -- the analyte charge -- was then assumed to be the key parameter most likely affected by PEG on the sensor surface. Qualitatively, the PEG effect can be explained within the Donnan potential picture, if the combination of recognition molecules, linker molecules and PEG is assumed to form a surface layer with a nearly constant potential. In this picture, the Debye screening starts to occur further away from the sensor surface, namely at the surface layer/electrolyte interface, which leads to a higher signal if the analyte binds within the PEG layer compared to the surface without PEG. To mathematically describe this, we introduced a pre-factor to the total net charge n0 of an analyte, namely the detectable charge qdet, representing the portion of analyte charges effectively detected by the sensor. We developed an equation to calculate the detectable charge depending on analyte size, position of the analyte with respect to the sensor surface, the surface layer thickness and the ionic strength. This equation was validated by comparing the values for the detectable charge with the potential shifts reported in four recent publications. The signal increase was found to be represented well by the increase in detectable charge when PEG is present on the surface, especially at high ionic strength. Based on this model, we proposed a design rule for immuno-FETs: PEG should be chosen that is at least as long as the combined length of linker, recognition molecule and analyte to detect at least half of the total analyte charge. Additionally, we extend this model to include the competitive binding between the recognition molecule to its analyte (high affinity) and the binding of ions to the same recognition molecule (low affinity). This model also considers that the analyte displaces ions upon binding following the Donnan theory. This competitive binding model describes calibration curve measurements more accurately than the commonly used Langmuir model.

Abbreviations and symbols

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BSA bovine serum albumin, FET field effect transistor, GFP green fluorescent protein, PSA prostate specific antigen, SAM self-assembled monolayer, SPR surface plasmon resonance, TSH thyroidstimulating hormone. In this work “linker” refers to COOH-EG8-thiol and “PEG” refers to 10 kDa mPEG-thiol.

Associated content The Supporting Information is available free of charge on the ACS Publications website at DOI: Derivation of concentration dependent model for surface potential (section I). Measuring the capacitance via impedance spectroscopy (section II). Investigating the influence of critical parameters in Langmuir-based model for concentration-dependent sensor response (section III). PEG-length determination from multi-parametric SPR (section IV). Surface layer characterization (section V). Calculation of detectable charge for published sensor layouts (section VI). Investigating the influence of critical parameters in competitive binding-based model for concentration-dependent sensor response (section VII). R script to calculate the detectable charge and the potential shifts (VIII). Funding Sources The research of the team “Nanomaterial-Based Biosensors” (NH, OG, and AT) at BioMed X Innovation Center is kindly sponsored by Roche Diagnostics GmbH. Acknowledgements The research of team “Nanomaterial-based biosensors” at BioMed X Innovation Center is kindly sponsored by Roche Diagnostics GmbH. The authors thank Dr. Pavel Kubalec and Dr. Tobias Oelschlaegel (Roche Diagnostics GmbH) for providing Anti-TSH IgG F(ab’)2 fragments. The authors are thankful to Prof. Andreas Dahlin and Dr. Gustav Emilsson for access and introduction to the BioNavis SPR Navi 220A at Chalmers University of Technology, Gothenburg, Sweden. The AFM measurements were performed on a JPK NanoWizard® 4 of the Molecular Imaging and Manipulation Facility, a core facility of the CMCB at Technische Universität Dresden.

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Table of contents Graphic

Tables and figures

Table 1: Capacitance is calculated from the complex impedance at the frequency where maximum potential shift occurs from electrochemical impedance spectroscopy.

iS [mM]

Capacitance [µF/cm²] no PEG

with PEG

10

13.5 ± 0.1

13.2 ± 0.2

150

12.1 ± 0.2

12.3 ± 0.02

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Figure 1: A) Schematic representation of ions of concentration cIon from the electrolyte migrating towards the solid electrode surface (indicated by the arrow). B) Potential distribution vs. distance from electrode surface (x = 0) with the potential decaying by 1/e at the Debye length (1/κ). C) Schematic representation of ion distribution proposed by Ohshima. A surface layer separates the solid electrode surface from the liquid electrolyte (blue). Ions are immobilized in the surface layer resulting in a nearly stable Donnan potential ΨDON. (D) ΨDON drops sigmoidal close to the surface layer – electrolyte interface. The decay is determined by the Debye length 1/κ but starts to decay much further away from the sensor surface compared to B.

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Figure 2: A) Schematic representation of the detectable charge vs. the distance of analyte from surface. Because of their size (dAnalyte), protein analytes cannot be assumed as point charges. The analyte can theoretically bind at any position with respect to the electrode surface (x0). B) The surface potential drops with distance from the surface following a sigmoidal decay, depending on the length of surface layer d and ionic strength (solid line). The detectable charge qdet is defined as the integral of the potential distribution in the bounds of the analyte position (shaded area under the curve). C) qdet is plotted as function x0 for a sensor without PEG (red) and a sensor with PEG (blue). A 3x increase of the detectable charge is observed (arrow) at a distance from the surface consistent with the position where the analyte is expected to bind to the capture antibody.

Table 2: Published experimental results of direct analyte detection on sensors with and without PEG in different ionic strength buffers. The ratio of read-out signal with and without PEG is calculated from the maximum potential shifts reported in the noted references. Detectable charge qdet is calculated from eq. 7 to 9 using dimensions derived from sensor layout.

Recognition Analyte Ionic Molecule strength [mM]

Potential shift ΔVmax [mV] No PEG

Ratio ΔVmax

Ref.

With PEG

qdet, No PEG

With PEG

F(ab)2

TSH

10

17

51

1:3

11

0.36

0.60

F(ab)2

TSH

150

4

12

1:3

11

0.21

0.66

F(ab)2

TSH

100

4

15

1:3.8

12

0.24

0.91

Nanobody

GFP

1

30.2

51.9

1:1.7

8

0.74

0.91

Nanobody

GFP

100

8.1

23.3

1:2.8

8

0.35

0.99

Aptamer

PSA

150

1.2

5.2

1:4.3

3

0.21

0.91

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Figure 3: Modelling of detectable charge for three hypothetical analytes from small (1 nm) over medium sized (5 nm) to large (10 nm). The detectable charge qdet is shown for each analyte paired to a selection of recognition of molecules as a function of PEG length.

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Figure 4: A) Schematic representation of the parameters considered in the model for potential shift based on Langmuir binding. The analyte of bulk concentration cAnalyte, total net charge n0 and detectable charge qdet bound by a recognition molecule of surface density NR with dissociation constant KD. B) TSH concentration dependent potential shift as measured by GutierrezSanz and co-workers (points) and as simulated using the Langmuir binding-based model (line). In the model NR is 2.1x1016/m2 on SAM without PEG (red lines) and 2.3x1016/m² on SAM with PEG (blue lines), KD is 0.19 nM, n0 is 5 per analyte 32 and the calculated qdet is noted next to the simulated data. C) Schematic representation of the parameters considered in the model based on competitive binding. Additional to the parameters in A, we also consider the unspecific binding of ions from the buffer with bulk concentration cIons to the recognition molecule with dissociation constant K1 and to the remaining surface groups of density NS with dissociation constant K2. D) TSH concentration dependent potential shifts as measured by GutierrezSanz and co-workers (points) and as simulated using the competitive binding-based model (lines). The same values for NR, KD, n0 and qdet were used as in B. K1 and K2 are assumed to be 1*10-4 M representing weak interaction. NS is assumed to be 10 % of total surface. In B) and D) the calculated capacitances from Table 1 were used.

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