Chapter 2
A recognition event is invisible until a transducer turns it into current, voltage, light, frequency or heat. This chapter works through the physics behind each transducer family in WIA-BIO-011 §4, shows how each one is recorded in BiosensorConfig, and ends with a practical guide to choosing between them.
Chapter 1 ended at the recognition layer: an enzyme turning over its substrate, an antibody capturing its antigen, a probe hybridizing with its target. None of these events can be read directly. What the reader instrument sees is a physical quantity that the event changes: electrons crossing an electrode interface, a shift in electrode potential, a change in light absorbed or emitted, a drop in the resonance frequency of a crystal, or a small rise in temperature. The transducer defines which of these quantities is measured. It therefore also fixes the units of the raw signal, the kinds of noise that dominate, the interferences to design against, and the environmental variables that must be controlled.
WIA-BIO-011 organizes transducers in two places. The specification (§4) gives the governing equations for electrochemical, optical, piezoelectric and thermal sensing. The type definitions give the machine-readable vocabulary: BiosensorType (electrochemical, optical, piezoelectric, thermal, impedance, calorimetric), the subtypes ElectrochemicalType and OpticalType, and a handful of transducer fields in BiosensorConfig. This chapter covers physics only. Calibration statistics, detection limits and the other performance metrics are derived from the resulting signals in Chapter 3.
An amperometric sensor holds the working electrode at a fixed potential and measures the current that flows when an electroactive species is oxidized or reduced at its surface. Once that potential is high enough to consume every arriving molecule, the current no longer depends on electrode kinetics. It is set by how fast the species diffuses to the surface. Spec §4.1.1 writes this as Faraday's law combined with Fick's first law:
I = n · F · A · D · (dC/dx)
I current (A)
n electrons transferred per molecule
F Faraday constant, 96 485 C/mol (BIOSENSOR_CONSTANTS.FARADAY_CONSTANT)
A electrode area (cm²)
D diffusion coefficient (cm²/s)
dC/dx concentration gradient at the surface (mol/cm⁴)If the concentration gradient is approximated as linear across a diffusion layer of thickness δ, with the surface concentration held near zero, then dC/dx ≈ C/δ and the current becomes proportional to the bulk concentration C. That proportionality is why amperometric sensors so often have a linear calibration. A worked order-of-magnitude example, with illustrative values: hydrogen peroxide (n = 2, D ≈ 1.4 × 10⁻⁵ cm²/s) at 1 mM (1 × 10⁻⁶ mol/cm³), on a 3 mm disc electrode (A ≈ 0.071 cm²), with δ = 50 µm, gives I ≈ 2 × 96 485 × 0.071 × 1.4 × 10⁻⁵ × (10⁻⁶ / 5 × 10⁻³) ≈ 3.8 × 10⁻⁵ A, or about 38 µA. A real enzyme electrode gives much less, because only a fraction of the analyte is converted to peroxide and a diffusion-limiting membrane deliberately slows transport. That is the same membrane that raises the apparent Km,app in Chapter 1.
When the potential is stepped rather than held, the current decays as the depletion zone grows. For a planar electrode in unstirred solution, the Cottrell equation describes this decay: I(t) = nFAC·√(D/(πt)). Many disposable strip readers sample the current at a fixed time after the step for exactly this reason. The reading is proportional to C only if the sampling time is identical from strip to strip. The sampling time therefore belongs in the device's measurement method, even though v1.0 has no dedicated field for it.
A potentiostat controls the potential of the working electrode (WE) relative to a reference electrode (RE), which carries almost no current and so keeps a stable potential. The current needed to sustain the reaction flows between the WE and a counter electrode (CE). Separating the roles this way stops the potential being dragged by ohmic drop and by polarization of the current-carrying electrode. Low-cost test strips often merge CE and RE into one Ag/AgCl pseudo-reference. That works because strip currents are small and the measurement is short.
Field in BiosensorConfig | Allowed values (v1.0) | Engineering notes |
|---|---|---|
workingElectrode | platinum, gold, carbon, silver, glassy-carbon | Platinum catalyses peroxide oxidation. Gold suits thiol self-assembled monolayers. Carbon inks dominate screen-printed strips. |
referenceElectrode | ag-agcl, sce, calomel, pseudo-reference | SCE is the saturated calomel electrode, so sce and calomel overlap. This book recommends sce for the saturated form and keeping calomel only when the filling solution is different and documented. |
counterElectrode | platinum, gold, carbon | Should be at least as large as the WE, so that the counter reaction never limits the current. |
appliedPotential | number, in volts | Meaningful only together with referenceElectrode. Store 0.6, not 600. |
A potential without its reference is ambiguous. The saturated Ag/AgCl electrode sits at roughly +0.197 V and the SCE at roughly +0.241 V versus the standard hydrogen electrode, so the same numerical setting differs by about 44 mV between the two. Implementations should therefore treat appliedPotential and referenceElectrode as a pair and never compare potentials across sensors without converting them to a common reference.
Spec §4.1.1 uses the classic glucose oxidase (GOx) electrode as its example. The enzyme oxidizes glucose and reduces oxygen to hydrogen peroxide, and the electrode detects the peroxide at +0.6 V versus Ag/AgCl:
glucose + O₂ --(GOx)--> gluconolactone + H₂O₂
H₂O₂ --> O₂ + 2H⁺ + 2e⁻ (at the Pt working electrode, +0.6 V vs Ag/AgCl)The spec lists a linear range of 0–30 mM glucose and a response time of 5–30 s for this design. The weak point is the high potential. At +0.6 V, many other species in blood are oxidized directly at the electrode, with no enzyme involved. The usual culprits are ascorbate, urate and acetaminophen (paracetamol). Each adds current that the sensor cannot tell apart from peroxide current, so the reading is biased upwards. Three engineering answers developed over the history outlined in Chapter 1:
Chapter 3 shows how interference is quantified as a selectivity coefficient. The point here is physical: the choice of appliedPotential is a choice about which molecules the electrode will oxidize. A lower potential almost always buys selectivity, at the cost of needing a mediator or a better-wired enzyme.
A potentiometric sensor measures the potential difference between an indicator electrode and a reference electrode while essentially no current flows. The potential reports the activity of the species the membrane responds to, following the Nernst equation (spec §4.1.2):
E = E° + (RT / nF) · ln([Ox] / [Red])
At 25 °C, converting to base-10 logarithms:
E = E° + (59.16 mV / n) · log₁₀([Ox] / [Red])
R = 8.314 J/(mol·K) BIOSENSOR_CONSTANTS.GAS_CONSTANT
T = 298.15 K BIOSENSOR_CONSTANTS.STANDARD_TEMPERATURE
59.16 mV/decade BIOSENSOR_CONSTANTS.NERNST_SLOPEFor an ion-selective electrode (ISE), the same law is written in terms of the ion's activity a and charge z: E = constant + (2.303RT/zF)·log₁₀ a. The pH glass electrode is the best-known case. Its theoretical slope is −59.16 mV per pH unit at 25 °C, as spec §4.1.2 states. In biosensors, potentiometry is often coupled to an enzyme that changes a local ion activity. Urease is the classic example: it hydrolyses urea into ammonium and bicarbonate, and an ammonium-selective or pH-sensitive element follows the change.
Two consequences follow directly from the equation. First, the response is logarithmic. Each tenfold change in activity gives the same potential step, so potentiometric sensors cover wide concentration ranges but resolve small relative changes poorly. A 1 mV error at n = 1 is already about a 4 % error in activity. Second, the indicator membrane can have a very high electrical resistance, so the measuring amplifier needs a correspondingly high input impedance. Otherwise it draws current and the reading drifts.
The slope 2.303RT/nF is proportional to absolute temperature. The constant NERNST_SLOPE = 59.16 mV/decade is therefore valid only at 25 °C (298.15 K), which is exactly the value stored next to it in BIOSENSOR_CONSTANTS. The table below is computed from the SDK's own values of R and F.
| Temperature | T (K) | Slope, n = 1 (mV/decade) | Slope, n = 2 (mV/decade) |
|---|---|---|---|
| 0 °C | 273.15 | 54.20 | 27.10 |
| 20 °C | 293.15 | 58.16 | 29.08 |
| 25 °C | 298.15 | 59.16 | 29.58 |
| 30 °C | 303.15 | 60.15 | 30.07 |
| 37 °C | 310.15 | 61.54 | 30.77 |
| 40 °C | 313.15 | 62.13 | 31.07 |
The theoretical slope rises by about 0.2 mV/decade per kelvin for a monovalent ion. The error this causes is easy to underestimate. Suppose a sensor is calibrated at 25 °C and used at body temperature (37 °C) with no compensation. A true tenfold rise in activity produces a 61.54 mV step. The instrument divides that by 59.16 mV and reports 1.040 decades, a factor of 10^1.040 ≈ 10.97 instead of 10. That is roughly a 10 % overestimate one decade from the calibration point, and it grows with distance from it. Real electrodes add a second effect: E° and the reference electrode potential also depend on temperature, so a slope correction alone does not remove all of the error. The practical rule is to calibrate at the temperature of use, or to measure temperature and correct the slope with (RT/nF) at the actual T. The book's helper code in section 2.8 does exactly this.
Voltammetric sensors (voltammetric) sweep or pulse the potential and record current as a function of potential. The result shows where a species reacts as well as how much of it is present. In cyclic voltammetry, a reversible one-electron couple gives a separation between the anodic and cathodic peaks of about 59 mV at 25 °C. For a reversible couple under diffusion control, the peak current follows the Randles–Ševčík equation, ip = 2.69 × 10⁵ · n3/2 · A · D1/2 · C · v1/2 at 25 °C (A in cm², D in cm²/s, C in mol/cm³, scan rate v in V/s). Pulse techniques such as differential pulse and square-wave voltammetry take the difference between currents sampled before and after each pulse. This largely cancels the capacitive charging current and lowers the detection limit. Anodic stripping voltammetry pre-concentrates metal ions onto the electrode before the sweep, and is the workhorse for the heavy-metal applications discussed in Chapter 7.
A conductometric sensor (conductometric) measures a change in solution conductance, typically between two interdigitated electrodes driven with an alternating voltage to avoid polarization. It suits enzyme reactions that create or consume ions, such as urease producing ammonium and bicarbonate. The drawback is that conductance responds to every ion. The sample's background ionic strength must be stable, or a differential pair with an enzyme-free reference electrode must be used.
EIS applies a small sinusoidal voltage over a range of frequencies and measures the complex impedance (spec §4.1.3):
Z(ω) = R + jX = |Z| · e^(jφ) ω = 2πf, j = √(−1)
Randles equivalent circuit:
Rs +-----||------------+
o---/\/\/\---------+ Cdl +---o
+---/\/\/\---[ W ]--+
Rct Warburg
Rs solution resistance
Cdl double-layer capacitance (often a constant-phase element in practice)
Rct charge-transfer resistance
W Warburg element (diffusion), Z_W = σ(1 − j)/√ωOn a Nyquist plot (−X against R), the circuit traces a semicircle followed by a 45° line. The high-frequency intercept gives Rs, the diameter of the semicircle gives Rct, and the 45° tail at low frequency comes from diffusion. The top of the semicircle falls at ω = 1/(Rct·Cdl). With illustrative values of Rct = 2 kΩ and Cdl = 1 µF, that is 500 rad/s, or about 80 Hz. The measurement frequency window must bracket this point, or Rct cannot be extracted reliably.
Impedance is the main route to label-free affinity sensing in electrochemistry. In the faradaic mode, a redox probe such as the ferri/ferrocyanide couple is added to the solution. When antibodies, aptamers or DNA probes on the electrode bind their target, the captured layer hinders electron transfer to the probe and Rct increases. The analytical signal is ΔRct, or the relative change ΔRct/Rct,0, which compensates for differences between electrodes. In the non-faradaic mode, no redox probe is used and the sensor tracks the change in interfacial capacitance. Both modes are sensitive to nonspecific adsorption, because any material that reaches the surface changes the impedance. The blocking and passivation measures from Chapter 1 therefore matter even more here than in amperometry.
Impedance also measures cells. Intact cell membranes are poor conductors at low frequency, so cells that settle on or pass between electrodes change the measured impedance. This is the basis of the README's "Impedance" row (cell counting and viability, typical LOD 10³–10⁶ cells/mL per README). Note that v1.0 offers two ways to say "impedance": the top-level BiosensorType value impedance and the subtype electrochemicalType: 'impedimetric'. The SDK does not check either one. This book recommends type: 'electrochemical' with electrochemicalType: 'impedimetric' for electrode-based EIS, which keeps all electrode fields meaningful, and reserving type: 'impedance' for whole-cell impedance counters without a conventional three-electrode cell.
Absorbance sensors measure how much light a coloured product absorbs. The Beer–Lambert law (spec §4.2.1) gives A = ε·c·l, with molar absorptivity ε (M⁻¹·cm⁻¹), concentration c (M) and path length l (cm). Transmittance is T = I/I₀ = 10^(−A). A familiar example is NADH, with ε ≈ 6 220 M⁻¹·cm⁻¹ at 340 nm, which many dehydrogenase assays follow. At 0.1 mM in a 1 cm cuvette, A ≈ 0.62, which is easy to measure. In a microfluidic channel only 100 µm deep, the same sample gives A ≈ 0.006, a change in transmitted light of about 1.4 %. This is the central problem of miniaturized absorbance sensing: shrinking the sample shrinks the path length, and the signal falls with it. Designers answer with longer folded channels, amplifying enzyme labels that produce more coloured product per binding event, or a switch to fluorescence. At the other end of the range, the linear law breaks down at high absorbance, because stray light and polychromatic sources dominate. Upper limits of around 1 absorbance unit are common in practice, depending on the instrument.
A fluorophore absorbs at one wavelength and emits at a longer one; the difference is the Stokes shift. Spec §4.2.2 gives the emitted intensity as F = Φ·I₀·ε·c·l, with quantum yield Φ (0–1) and excitation intensity I₀. This expression is the low-absorbance limit of the more general form F = k·Φ·I₀·(1 − 10^(−εcl)), where k is the fraction of emitted light the optics collect. When εcl is small, 1 − 10^(−εcl) ≈ 2.303·εcl, and the signal is linear in c. The factor 2.303 and the collection efficiency k disappear into the instrument's calibration constant. Above an absorbance of a few hundredths, the sample begins to absorb its own excitation and emission light (the inner-filter effect), and the calibration curve bends downward. This is a physical reason for keeping fluorescent assays dilute.
Fluorescence usually reaches lower detection limits than absorbance, for a simple reason: the detector looks for light against a dark background, rather than for a small dip in a bright beam. The price is sensitivity to background autofluorescence from the sample and plastics, to photobleaching, and to drift in excitation intensity. BiosensorConfig.wavelength records the optical window as { excitation, emission } in nanometres. Fluorescein, for example, is excited near 490 nm and emits near 515–520 nm.
Förster resonance energy transfer is a non-radiative transfer of energy from an excited donor to a nearby acceptor. Its efficiency depends steeply on the donor–acceptor distance r (spec §4.2.2): E = R₀⁶ / (R₀⁶ + r⁶), where the Förster radius R₀ (typically 2–10 nm) is the distance at which half the energy is transferred. The sixth-power dependence makes FRET a molecular ruler. A binding event that brings the pair together or pushes it apart switches the signal from one state to the other.
| Distance r | FRET efficiency E | Interpretation |
|---|---|---|
| 0.5 R₀ | 0.985 | Almost complete transfer. Donor emission is quenched. |
| 1.0 R₀ | 0.500 | Midpoint, the most distance-sensitive region. |
| 1.5 R₀ | 0.081 | Weak transfer. |
| 2.0 R₀ | 0.015 | Essentially no transfer. |
Structure-switching aptamers and hybridization probes such as molecular beacons use this principle. Target binding changes the probe's conformation and therefore the donor–acceptor distance. Ratiometric readout (acceptor emission divided by donor emission) cancels much of the variation in excitation intensity and optical alignment, so it is preferred over single-channel intensity.
In luminescence (luminescence), light comes from a chemical or enzymatic reaction rather than from an excitation source. Examples are luminol oxidation catalysed by horseradish peroxidase, and firefly luciferase, which consumes ATP. With no excitation light there is no scattered background, which is why luminescent assays can reach very low detection limits with simple optics. The emission is transient, though, so timing must be controlled precisely.
Colorimetric sensors (colorimetric) produce a colour visible by eye or by a camera. Examples are an enzyme label converting a chromogenic substrate, or gold nanoparticles changing colour from red to blue as they aggregate. The lateral-flow test is the most widespread colorimetric format. The sample wicks along a strip, labelled antibodies bind the target, and the complex is captured at a test line where the accumulated label becomes visible. v1.0 has no separate lateral-flow value. This book recommends opticalType: 'colorimetric' for gold- or latex-labelled strips and 'fluorescence' for strips with fluorescent labels. A strip reader measures the line intensity by reflectance, which is not transmitted absorbance, so Beer–Lambert holds only approximately. Such readers are calibrated empirically against standards, usually with the nonlinear models of Chapter 3.
Surface plasmon resonance (SPR) detects binding at a thin gold film without any label. In the common Kretschmann configuration, polarised light passes through a prism and reflects off the back of a gold film. At one particular angle of incidence the light couples into surface plasmons, the collective oscillations of electrons at the metal–liquid interface, and the reflected intensity drops sharply. That resonance angle depends on the refractive index of the medium immediately next to the gold. The plasmon field is evanescent: it decays exponentially away from the surface over a characteristic depth of roughly 200 nm, the value the spec gives. Only changes within that thin region affect the resonance. When analyte binds to receptors on the gold, the local refractive index rises and the resonance angle shifts. Recording this shift over time gives a real-time binding curve, from which association and dissociation rates, and hence the affinity constants of Chapter 1, can be extracted.
Two quantities are easy to confuse, and spec §4.2.3 confuses them:
The spec also gives the formula "Δθ = m × Δn × d". This is not a standard physical relation, and this book does not use it. Correctly stated, the angle shift is approximately the bulk sensitivity multiplied by an effective refractive-index change, Δθ ≈ S·Δneff. For a thin adsorbed layer much thinner than the decay depth, Δneff is small: it grows with the layer's thickness relative to the evanescent decay length and with the index contrast between layer and buffer. This is why SPR responds well to proteins bound close to the surface, and poorly to large particles or cells whose bulk lies outside the field.
The same physics explains why SPR instruments need tight temperature control and a reference channel. The refractive index of water changes by roughly 1 × 10⁻⁴ RIU per kelvin near room temperature. To resolve 10⁻⁶ RIU, the temperature must therefore be steady to about 0.01 K, or its effect subtracted using a reference surface that sees the same buffer without the specific receptor. The reference channel also removes the bulk refractive-index jump when sample and running buffer differ slightly in composition.
A quartz crystal microbalance (QCM) is a thin disc of AT-cut quartz between two electrodes, driven at its thickness-shear resonance. Mass added to the surface lowers the resonance frequency. For a thin, rigid, uniform film, the Sauerbrey equation (spec §4.3.1) relates the frequency shift to the areal mass:
Δf = −2 f₀² · Δm / (A · √(μq · ρq)) = −Cf · Δm / A
μq = 2.947 × 10¹¹ g·cm⁻¹·s⁻² (shear modulus of AT-cut quartz)
ρq = 2.648 g/cm³ (density of quartz)
√(μq·ρq) ≈ 8.83 × 10⁵ g·cm⁻²·s⁻¹
Cf = 2 f₀² / √(μq·ρq)
f₀ = 5 MHz → Cf ≈ 5.66 × 10⁷ Hz·cm²/g = 56.6 Hz·cm²/µg
f₀ = 10 MHz → Cf ≈ 2.26 × 10⁸ Hz·cm²/g = 226 Hz·cm²/µgNote the correction. Spec §4.3.1 attributes 2.26 × 10⁸ Hz·cm²/g to a 5 MHz crystal, but that is the 10 MHz value. Because Cf scales with f₀², doubling the fundamental frequency quadruples the constant. Using the wrong constant on a 5 MHz sensor makes every mass estimate four times too small.
| Worked case (Δm/A = 10 ng/cm²) | 5 MHz crystal | 10 MHz crystal |
|---|---|---|
| Cf (Hz·cm²/µg) | 56.6 | 226 |
| Frequency shift Δf | −0.57 Hz | −2.26 Hz |
| Mass per 1 Hz shift | ≈ 17.7 ng/cm² | ≈ 4.4 ng/cm² |
| Relative shift Δf/f₀ | ≈ 1.1 × 10⁻⁷ | ≈ 2.3 × 10⁻⁷ |
The table shows why mass resolution in the ng/cm² range places heavy demands on the electronics. A shift of half a hertz on a 5 MHz carrier is a change of about one part in ten million, so frequency counting must be stable and averaged, and temperature must be controlled. Higher-frequency crystals are more sensitive but thinner and more fragile.
The Sauerbrey equation has firm validity limits, and biosensing often breaks them:
v1.0 defines piezoelectric as a BiosensorType, but BiosensorConfig has no field for f₀, the active area or the overtone. Because these values determine how Hz converts to ng/cm², they must travel with the calibration record. Until a future version adds fields for them, this book recommends storing them in the device documentation and in a clearly named extension object on the calibration record (Section 4.7), because CalibrationData has no free-text notes field.
Almost every enzymatic reaction releases or absorbs heat. A calorimetric biosensor, often called an enzyme thermistor, immobilises the enzyme in a small column or on a chip and measures the temperature rise of the fluid passing through it. Spec §4.4.1 gives the chain of relations:
Q = n · ΔH heat released (J), n = moles converted, ΔH = molar enthalpy (J/mol)
ΔT = Q / (m · Cp) temperature rise of a mass m (g) with heat capacity Cp (J/(g·K))The spec writes the first line as Q = n × ΔH × V. That is dimensionally consistent only if n is a concentration (mol/L) and V a volume (L), so that n·V is again a quantity of substance. This book uses n directly as moles converted.
An illustrative calculation shows the order of magnitude. Take a reaction enthalpy of −80 kJ/mol, a round figure of the size typical for enzyme reactions. Suppose 1 µmol of substrate is converted completely within 1 g of aqueous solution (1 mL of a 1 mM sample, Cp ≈ 4.18 J/(g·K)). Then Q ≈ 10⁻⁶ × 8 × 10⁴ = 0.08 J and ΔT ≈ 0.08 / 4.18 ≈ 0.019 K, about 19 mK. At 10 µM the same calculation gives about 0.2 mK. In a real flow cell, conversion is incomplete and heat escapes to the surroundings, so the measured rise is smaller still. A thermal biosensor therefore needs temperature resolution in the millikelvin range or better. Negative-temperature-coefficient thermistors, whose resistance typically changes by a few percent per kelvin near room temperature, are connected in a bridge with a matched reference thermistor so that fluctuations in ambient temperature cancel.
The attraction of the method is its generality and its tolerance of the sample. Heat is measured, not light or electron transfer, so coloured, turbid or electroactive samples cause no optical or redox interference. Signal can be increased by coupling enzymes. Adding catalase to a GOx column, for instance, decomposes the peroxide and adds its enthalpy to the total. The drawbacks are thermal isolation, sensitivity to ambient temperature and slow equilibration. Thermal sensors appear most often in process monitoring rather than in handheld devices, consistent with the README's "Thermal" row (enzyme activity and metabolism, typical LOD µM–mM per README).
As with impedance, v1.0 provides two overlapping labels: thermal and calorimetric are both top-level BiosensorType values. This book recommends calorimetric for sensors that infer a reaction enthalpy, and thermal for other temperature-based transduction, for example sensing a change in thermal conductivity.
The README's type table lists each transducer with its transduction principle, applications and typical LOD. The table below extends it with engineering criteria that often decide the choice in practice. The LOD column repeats the README's indicative ranges. The other columns are this book's qualitative assessment, not WIA requirements.
| Transducer (enum) | Measured quantity | Typical LOD (per README) | Label needed? | Reader cost / miniaturization | Main matrix sensitivities |
|---|---|---|---|---|---|
Amperometric (electrochemical / amperometric) | Current at fixed potential | nM–µM | No (enzyme product) or enzyme label | Very low cost. Easily miniaturized (strips, wearables). | Electroactive interferents, dissolved O₂, temperature |
Potentiometric (potentiometric) | Potential at zero current | Not listed; logarithmic response over wide ranges | No | Low cost; needs a stable reference electrode. | Other ions, temperature (slope), reference drift |
Impedimetric / EIS (impedimetric, impedance) | Complex impedance vs frequency | 10³–10⁶ cells/mL for cell counting | No | Moderate; needs a frequency-response analyser. | Nonspecific adsorption, ionic strength |
| Optical: absorbance / colorimetric | Light absorbed or reflected | pM–nM for the optical group | Usually an enzyme or particle label | Low cost (phone cameras, LEDs). Path length limits miniaturization. | Sample colour, turbidity, haemolysis |
| Optical: fluorescence / FRET / luminescence | Emitted light | pM–nM for the optical group | Usually a fluorophore or luminogenic label | Moderate; filters and dark housing required. | Autofluorescence, photobleaching, inner filter |
SPR (spr) | Refractive index near a gold film | pM–nM for the optical group | No | High; strict optical and thermal control. | Bulk index changes, temperature, nonspecific binding |
QCM (piezoelectric) | Resonance frequency shift | ng/mL | No | Moderate; fragile crystals and flow cell. | Viscosity, temperature, viscoelastic layers |
| Thermal / calorimetric | Temperature rise | µM–mM | No | Moderate; bulky thermal isolation. | Ambient temperature, flow rate |
In practice the choice follows a handful of questions, asked roughly in this order:
BiosensorConfig
Once the transducer is chosen, its identity and key operating conditions go into the configuration. The following examples are illustrative configurations: the analyte names and values are chosen to match this chapter's discussion, not taken from a certified device. The // lines are reading aids and not part of the JSON.
// Amperometric GOx electrode (first generation, peroxide detection)
{
"type": "electrochemical",
"electrochemicalType": "amperometric",
"biorecognitionElement": "glucose-oxidase",
"targetAnalyte": "glucose",
"analyteCategory": "metabolite",
"workingElectrode": "platinum",
"referenceElectrode": "ag-agcl",
"counterElectrode": "platinum",
"appliedPotential": 0.6,
"sampleType": "blood",
"temperature": 25,
"pH": 7.0
}
// Fluorescent structure-switching aptamer (FRET readout)
{
"type": "optical",
"opticalType": "fret",
"biorecognitionElement": "aptamer",
"targetAnalyte": "thrombin",
"analyteCategory": "protein",
"wavelength": { "excitation": 490, "emission": 520 },
"sampleType": "serum",
"temperature": 25
}
// Faradaic EIS immunosensor
{
"type": "electrochemical",
"electrochemicalType": "impedimetric",
"biorecognitionElement": "antibody",
"targetAnalyte": "C-reactive protein",
"analyteCategory": "protein",
"workingElectrode": "gold",
"referenceElectrode": "ag-agcl",
"counterElectrode": "platinum",
"sampleType": "serum"
}
Two points about the reference SDK are worth knowing now. Chapters 4 and 5 give the full picture. First, validateConfig checks only that type, biorecognitionElement and targetAnalyte are present. It does not check that an opticalType belongs to an optical sensor, that appliedPotential has a referenceElectrode, or that wavelength has emission longer than excitation. Second, the SDK never reads electrochemicalType, opticalType, appliedPotential or wavelength during measurement. They are descriptive metadata. The consistency checks are therefore the implementer's job, and physical conversions such as the Nernst slope at the actual temperature or the Sauerbrey mass conversion belong in application code. The following helper functions are this book's own code, not part of the @wia/bio-011 API. They use only the published constants:
import { BIOSENSOR_CONSTANTS as K, BiosensorConfig } from '@wia/bio-011';
/** Nernst slope in mV/decade at temperature tC (°C) for charge n. */
export function nernstSlope(tC: number, n = 1): number {
const T = tC + 273.15;
return (Math.LN10 * K.GAS_CONSTANT * T / (n * K.FARADAY_CONSTANT)) * 1000;
}
// nernstSlope(25) ≈ 59.16 nernstSlope(37) ≈ 61.54 nernstSlope(37, 2) ≈ 30.77
/** Sauerbrey areal mass (ng/cm²) from a frequency shift (Hz), f0 in Hz. */
export function sauerbreyMass(deltaF: number, f0: number): number {
const sqrtMuRho = Math.sqrt(2.947e11 * 2.648); // g·cm⁻²·s⁻¹
const cf = (2 * f0 * f0) / sqrtMuRho; // Hz·cm²/g
return (-deltaF / cf) * 1e9; // ng/cm²
}
// sauerbreyMass(-0.566, 5e6) ≈ 10 sauerbreyMass(-2.264, 10e6) ≈ 10
/** Book-level consistency checks the v1.0 SDK does not perform. */
export function checkTransducerConfig(c: BiosensorConfig): string[] {
const issues: string[] = [];
if (c.opticalType && c.type !== 'optical')
issues.push('opticalType set on a non-optical sensor');
if (c.electrochemicalType && c.type !== 'electrochemical')
issues.push('electrochemicalType set on a non-electrochemical sensor');
if (c.appliedPotential !== undefined && !c.referenceElectrode)
issues.push('appliedPotential has no referenceElectrode');
if (c.appliedPotential !== undefined && Math.abs(c.appliedPotential) > 2)
issues.push('appliedPotential looks like mV; the field is in volts');
const w = c.wavelength;
if (w?.excitation !== undefined && w?.emission !== undefined && w.emission <= w.excitation)
issues.push('emission wavelength should exceed excitation (Stokes shift)');
return issues;
}The ±2 V bound in the last check is a book heuristic for catching values entered in millivolts. It is not a WIA limit. Aqueous electrochemistry rarely goes beyond this window, because water itself is oxidized or reduced there.
Several formulas in spec §4 need a correction or a qualification before they can be used in engineering calculations. The table collects the ones this chapter relies on. The complete v1.0 errata list is in Chapter 8.
| Spec location | As written in v1.0 | How this book uses it |
|---|---|---|
| §4.2.2 fluorescence | F = Φ·I₀·ε·c·l | Valid only at low absorbance. The factor 2.303 and the optical collection efficiency are absorbed into the calibration constant. |
| §4.2.3 SPR | Δθ = m × Δn × d; "sensitivity 10⁻⁶–10⁻⁷ RIU" | Not used as a physical law. SPR is described qualitatively; 10⁻⁶–10⁻⁷ RIU is treated as a resolution, and sensitivity is given in deg/RIU. |
| §4.3.1 QCM | Cf ≈ 2.26 × 10⁸ Hz·cm²/g "for 5 MHz" | This is the 10 MHz value. At 5 MHz, Cf ≈ 5.66 × 10⁷ Hz·cm²/g (56.6 Hz·cm²/µg). |
| §4.4.1 calorimetry | Q = n × ΔH × V | Q = n·ΔH with n in moles. The ×V form holds only if n is a concentration. |
| §4.1.2 potentiometry | 59.16 mV/n at 25 °C | Correct at 25 °C only. The slope scales with absolute temperature (61.54 mV/decade at 37 °C for n = 1). |
Chapter 3 takes the raw signals produced by these transducers and turns them into calibrated, quantified results. It covers baseline correction, filtering, regression, and the performance metrics that let different sensors be compared on equal terms.