6.4.3 Protein-FET - Streptavidin-Biotin-FET

The chemist Gerhardus Johannes Mulder was the first to describe proteins and Jöns Jakob Berzelius the first naming them in $1838$. Proteins play a key role in living organsims. They are like other biological macromolecules, such as polysaccharides and nucleic acids, essential parts of an organism and participate in an endless list of processes within a cell. Numerous proteins are enzymes catalyzing biochemical reactions and thus vital to metabolism. They also exhibit structural or mechanical functions, such as actin and myosin in muscles or the proteins in the cytoskeleton forming a system of scaffolding which maintains the cell shape. Proteins are also substantial in cell signaling, immune responses, cell adhesion, and the cell cycle.

Proteins are linear polymers and consist of a series of up to $20$ different L-$\alpha$-amino acids. All amino acids exhibit common strucutral features like an $\alpha$-carbon bonded to an amino group, a carboxyl group, and a variable side chain. Their three-dimensional structures were first determined by Perutz and Kendrew via x-ray diffraction analysis in $1962$, awarded with the Nobel prize in chemistry for their discoveries.

Streptavidin is a tetrameric protein purified from the bacterium streptomyces avidinii and each subunit is able to bind biotin with equal affinity (Fig. 6.14, Fig. 6.15). It is exploited widely in molecular biology through its extraordinarily strong affinity for biotin. It also possesses one of the strongest non-covalent interactions known in nature. Among the most common uses are the purification or detection of various biomolecules. The strong streptavidin-biotin bond can be utilized to attach various biomolecules to one another or onto a solid support.

Figure 6.14: Scheme of the tetrameric protein streptavidin and biotin.

As mentioned before proteins play a major role in a living organism. Therefore, various kinds of reaction pairs are of interest and have been studied comprehensively, like detection of DNA [17], [150], [151], cancer markers [152], proteins, e.g. biotin-streptavidin [153], [154], [155], [156], albumin [157], and transferrin [158].

The biotin-streptavidin reaction pair is modeled with the physics-based bottom-up approach of Section 6.4.2.1. Here, once more the charge and dipole moment for a single molecule (biotin/streptavidin) (see for example Figure 6.15, [235]) is obtained and extrapolated to the mean charge density and the mean dipole moment density of the boundary layer, bridging the gap between the Angstrom length scale of the biomolecules and the micrometer dimensions of the FET [219], [220], [236]. The x-axis is chosen parallel to the oxide surface, while the y-axis points into the liquid. $\psi(0-)$ describes the potential in the oxide, while $\psi(0+)$ relates to the potential in the solute. The first equation (6.3) introduces the jump in the field, while the second (6.4) describes the dipole moment which causes a shift of the potential taken into account by adjusting the potential in the analyte.

Figure 6.15: Biotin-streptavidin complex [2] on the oxide surface. Two iso-surfaces for plus and minus $0.03\, k_{B}T/q \AA{}^{2}$ are shown.

Three different oxid types were utilized as dielectric. $SiO_{2}$as a reference, $Al_{2}O_{3}$, and $T\!a_{2}O_{5}$as possible high-k materials, with relative permitivies of $3.9$, $10$, and $25$ respectively. Sodium chloride was chosen as solute at $\mathrm{pH}\,7$. For each dielectric several simulation runs were performed such as the unprepared state (only water and salt), the prepared but unbound state (water, salt and biotin), and the bound state, when the chemical reaction has occured (water, salt, and biotin-streptavidin). Furthermore, for every dielectric two sets of mean distances between the molecules ( $\lambda =10\rm {nm}$, $\lambda =15\rm {nm}$) and two different orientations in relation to the surface ( $0^{\circ}\dots$ perpendicular to the surface and $90^{\circ}\dots$ parallel to the surface) were considered. The data for biotin and streptavidin were obtained from [2] and exploited for their charges and dipole moments. The ProteinFETs output curves were computed for every parameter combination mentioned before, under the assumption of a $100\%$ binding efficency. The potential of the reference electrode was set to $0.4$V, shifting the FET into moderate inversion as proposed by [160].

Fig. 6.16, Fig. 6.17, and Fig. 6.18 show a decrease in the output current for biotin attached to the surface in comparison to the unprepared surface. This downward shift for the bound state in comparison to the unbound state is caused by the increase of negative charges at the interface, which is consistent with the difference between the curves for $\lambda=10\mathrm{nm}$ and $\lambda=15\mathrm{nm}$, since for $10\mathrm{nm}$ the molecules are more dense than by $15\mathrm{nm}$.

One can learn from Fig. 6.16, Fig. 6.17, and Fig. 6.18 the bigger the $\varepsilon_{r}$ of the dielectric the bigger is the output current. Thus high-k materials enable stronger output signals. However, according to [237], higher $\varepsilon_{r}$ dielectric constants may be influenced by higher trap densities and thus lead to a decreased signal-to-noise ratio. Therefore a compromise between an increased output signal and a good signal-to-noise ratio has to be found.

Figure 6.16: Output curve for $\rm {SiO_{2}}$ for unprepared, prepared but unbound, and bound state at $\lambda =10\rm {nm}$ and $\lambda =15\rm {nm}$, respectively.

Figure 6.17: Output curve for $\rm {Al_{2}O_{3}}$ for unprepared, prepared but unbound, and bound state at $\lambda =10\rm {nm}$ and $\lambda =15\rm {nm}$, respectively.

Figure 6.18: Output curve for $\rm {Ta_{2}O_{5}}$ for unprepared, prepared but unbound, and bound state at $\lambda =10\rm {nm}$ and $\lambda =15\rm {nm}$, respectively.

Fig. 6.19 illustrates the output curves as a function of dielectric and molecule orientation ($0^{\circ }$ denotes perpendicular to the surface and $90^{\circ }$ lying flat on the interface) yielding the lowest output curves for $0^{\circ }$ followed by $90^{\circ }$ and the curves without dipole moment for each group. Fig. 6.20 and Fig. 6.21 display the small signal resistance as a function of dielectric and molecule orientation, showing smaller values for higher relative permittivity $\varepsilon_{r}$. In agreement with the previous results depicted in Fig. 6.16, Fig. 6.17, and Fig. 6.18, a somewhat larger differential resistance is observed for the perpendicular molecule orientation. This has to be apprehended in the sense of the inhomogeneously charged biomolecules and in conjunction to the occuring dipole moment entering into the boundary conditions (6.4), thus yielding a difference in the output curves of the BioFET for different orientation angles in relation to the surface.

In order to increase the signal-to-noise ratio, the linker should be neutral or at least possess as little charge as possible. For instance, in the case of detecting streptavidin, biotin can be used as a binding agent. So biotin molecules are attached to the surface via a neutral linker. Streptavidin is then able to bind biotin and form a bound state at the interface. The charge difference between the unbound state of a single biotin, which is negatively charged with one single elementary charge and the bound state of biotin-streptavidin, which is negatively charged with five elementary charges, is large enough for detection. One also has to mention that due to the tetrameric nature of streptavidin it exhibits four binding sites for biotin as shown in Fig. 6.14. Thus, the linker for binding biotin to the surface should be short enough to impede binding several biotin molecules to a single molecule of streptavidin. If one has the freedom of choice in deciding, if biotin or streptavidin is initially is attached to the surface, I would recommend to attach biotin in advance of streptavidin. The relative change in charge will be bigger this way (from minus one elementary charge to minus five elementary charges) leading to an more pronunced change in the output signal and allows to attach further biotinilated molecules close to the interface^6.5.

The model shows a strong dependence on surface charges and indicates a detectable shift in the threshold voltage depending on their orientation related to the surface. It would be interesting to study an experimental setup introducing an additionall electric field parallel to the surface (e.g. extra isolated plates on the left and right side wall of the microfluidic), which enables to bend the molecules out of their equilibrium position into an arbitrary direction allowing the comparison with the results obtained from the simulations.

Figure 6.19: Output curves for $SiO_{2}$, $Al_{2}O_{3}$, and $T\!a_{2}O_{5}$for calculation without dipole moment, $0^{\circ }$ (perpendicular to surface), and $90^{\circ }$ (parallel to surface).

Figure 6.20: Small signal resistance for $SiO_{2}$, $Al_{2}O_{3}$, and $T\!a_{2}O_{5}$for calculation without dipole moment, $0^{\circ }$ (perpendicular to surface), and $90^{\circ }$ (parallel to surface) at biotin only.

Figure 6.21: Small signal resistance for $SiO_{2}$, $Al_{2}O_{3}$, and $T\!a_{2}O_{5}$for calculation without dipole moment, $0^{\circ }$ (perpendicular to surface), and $90^{\circ }$ (parallel to surface) at bound state (biotin-streptavidin).

Footnotes

... interface^6.5

due to the three remaing open binding sites of streptavidin for biotin