🔥 0 ⚡ 0 XP
← Back to Path
1 / 6

THE CATCH

Ions hide the charge you want to see

e−d/λD

A bound molecule's charge is screened by the mobile ions around it. The gate feels a charge at height d above the surface reduced by about e−d/λD, where λD is the Debye length. Charge farther than a few λD away is nearly invisible to the transistor.

Only charge within a few Debye lengths reaches the channel.

SCREENING IN NUMBERS

Signal fades with height

0.5 1 0 2 4 6 8 10 12 19% at 5 nm 1 mM: λD ≈ 10 nm 10 mM: λD ≈ 3 nm 150 mM: λD ≈ 0.8 nm height of the charge above the surface (nm) → fraction sensed ↑

In 150 mM saline, λD is about 0.8 nm, so a charge 5 nm up keeps about 0.2% of its effect. In 10 mM salt, λD is about 3 nm and the same charge keeps about 19%. Lower salt means a longer reach.

Diluting the sample lengthens the Debye length and revives the signal.

SIZE MISMATCH

Receptors can be taller than the reach

Antibody About 10 nm tall: most of its bound charge sits beyond a Debye length in saline
Fab fragment About 5 nm: half an antibody, and closer to the surface
Nanobody About 2–4 nm: a single small binding domain
Aptamer or DNA probe A few nm, and their charge is on the strand itself
Smaller receptors keep the target inside the Debye length.

WORKAROUNDS

Getting around screening

🧂

Dilute the sample

Lower the salt so λD grows, as long as the receptor still binds

🧫

Small receptors

Fab fragments, nanobodies, or aptamers keep the target close

〰️

High-frequency readout

Some designs measure fast, where ions cannot follow, so charge farther out is less screened

🧴

Polymer layer

A PEG brush can stretch the effective sensing distance

Each fix attacks the problem from a different side.

A WORKED CHOICE

Trade sensitivity for reach

1 mM: λD ≈ 10 nm

Diluting saline from 150 mM to 1 mM stretches λD from about 0.8 nm to about 10 nm. An antibody's charge at 8 nm then keeps about 43% of its effect, instead of well under 0.1%. The price: the sample is now diluted, and binding may be weaker at low salt.

Dilution helps the signal but changes the chemistry.

UNIT 20 STUDY COMPLETE

🔬

Ready for the Fab Challenge?

You've covered why salty samples hide bound charge, and what designers do about it.