Biophysics of Olfaction & Taste

Derivation: Binding Equilibrium and Dose-Response

The binding reaction follows simple mass-action kinetics:

$$O + R \xrightleftharpoons[k_{\text{off}}]{k_{\text{on}}} OR$$

At equilibrium, the rates of association and dissociation balance:

$$k_{\text{on}}[O][R] = k_{\text{off}}[OR]$$

Define the dissociation constant $K_d = k_{\text{off}}/k_{\text{on}}$. With total receptor concentration $[R]_T = [R] + [OR]$, the fractional occupancy is:

$$\boxed{\theta = \frac{[OR]}{[R]_T} = \frac{[O]}{K_d + [O]}}$$

This is a Langmuir isotherm. At $[O] = K_d$, half the receptors are occupied. Typical olfactory receptor $K_d$ values range from $\sim 1 \; \mu$M for high-affinity odorants to $\sim 1$ mM for weak agonists.

For cooperative binding (e.g., if receptor dimerisation occurs), the response is steepened by using the Hill equation:

$$\theta = \frac{[O]^{n_H}}{K_d^{n_H} + [O]^{n_H}}$$

where $n_H$ is the Hill coefficient. Values of $n_H > 1$ indicate positive cooperativity (sharper dose-response transition). The dynamic range of the response (10% to 90% occupancy) spans a concentration ratio of:

$$\frac{[O]_{90\%}}{[O]_{10\%}} = 81^{1/n_H}$$

For $n_H = 1$: ratio = 81 (~2 log units). For $n_H = 2$: ratio = 9 (~1 log unit). Higher cooperativity means sharper discrimination between odour concentrations.

Detection Thresholds

The olfactory system achieves remarkable sensitivity. Some thresholds for specific odorants:

• • Ethyl mercaptan (gas odorant): ~0.4 ppb in air
• • Geosmin (earthy smell): ~5 ppt in water
• • Androstenone (musky): ~0.2 ppb in air

At 0.4 ppb, ethyl mercaptan concentration is $\sim 10^{10}$ molecules/mL. With a sniff volume of ~200 mL, approximately $2 \times 10^{12}$ molecules reach the nasal cavity, of which ~2% reach the olfactory epithelium. With ~10 million olfactory neurons, this means ~4,000 molecules per neuron — more than enough for reliable detection.

Derivation: cAMP Cascade Amplification

Odorant binding activates the G-protein G$_{\text{olf}}$, which in turn activates adenylyl cyclase III (ACIII), producing cAMP that opens CNG channels:

$$OR^* \to G_{\text{olf}} \to \text{ACIII} \to \text{cAMP} \to \text{CNG channels}$$

Gain at each step:

• • 1 activated receptor $\to$ ~20 G$_{\text{olf}}$ molecules (before receptor is phosphorylated)
• • Each G$_{\text{olf}}$ activates 1 ACIII, producing ~50 cAMP molecules before GTP hydrolysis
• • Total: 1 OR* $\to$ ~1,000 cAMP molecules

The CNG channels in olfactory cilia are opened by cAMP binding with a Hill equation:

$$\boxed{I = I_{\max} \cdot \frac{[\text{cAMP}]^n}{K_{1/2}^n + [\text{cAMP}]^n}}$$

where $K_{1/2} \approx 4 \; \mu$M is the half-activation concentration and$n \approx 2$–$4$ is the Hill coefficient (each channel binds 4 cAMP molecules). The maximum current per cilium is $I_{\max} \approx 50$ pA. With ~20 cilia per ORN, the total maximum current is ~1 nA.

A secondary amplification step occurs: Ca$^{2+}$ entering through CNG channels opens Ca$^{2+}$-activated Cl$^-$ channels, which carry an additional depolarising current (the olfactory epithelium has high intracellular Cl$^-$). This roughly doubles the total transduction current.

Derivation: ORN Temporal Dynamics

The transduction current in an olfactory receptor neuron follows a time course determined by the cascade kinetics. For a step stimulus of odorant concentration $[O]$, the cAMP concentration rises and falls with characteristic kinetics:

$$\frac{d[\text{cAMP}]}{dt} = \alpha_{\text{AC}} \cdot \theta(t) - \beta_{\text{PDE}} \cdot [\text{cAMP}]$$

where $\alpha_{\text{AC}}$ is the adenylyl cyclase production rate (proportional to receptor occupancy $\theta$) and $\beta_{\text{PDE}}$ is the phosphodiesterase degradation rate. The steady-state cAMP level is:

$$[\text{cAMP}]_{\text{ss}} = \frac{\alpha_{\text{AC}} \cdot \theta}{\beta_{\text{PDE}}}$$

The time constant of the response is $\tau = 1/\beta_{\text{PDE}} \approx 100$–$200$ ms. This sets the temporal resolution of olfaction and explains why sniffing at ~5 Hz (200 ms per cycle) is near the limit of temporal resolution.

Adaptation in ORNs involves multiple mechanisms:

• • Fast adaptation (50–200 ms): Ca$^{2+}$entering through CNG channels binds calmodulin, which reduces the cAMP affinity of the channel:$K_{1/2}$ shifts from ~4 $\mu$M to ~20 $\mu$M
• • Medium adaptation (1–10 s): Ca$^{2+}$/CaM activates CaMKII, which phosphorylates ACIII, reducing cAMP synthesis rate
• • Slow adaptation (10–60 s): Receptor desensitisation via GRK3/beta-arrestin, reducing G-protein coupling

The net effect is that the ORN response to a sustained odour decays by ~80% within 10–20 seconds, which is why we quickly stop noticing persistent odours (e.g., entering a room with a strong smell).

One Receptor, One Neuron Rule

A remarkable finding is that each ORN expresses only a single type of olfactory receptor out of ~400 possible types. This is enforced by a feedback mechanism: expression of one receptor gene suppresses all others. Furthermore, all ORNs expressing the same receptor type converge their axons onto the same pair of glomeruli in the olfactory bulb (~1,800 glomeruli per bulb in humans, 2 per receptor type).

This creates a topographic map in the olfactory bulb where each glomerulus represents one receptor type. The spatial pattern of glomerular activation encodes the odour identity. Since there are ~10,000 ORNs per receptor type, each glomerulus integrates the signals from many neurons, improving the signal-to-noise ratio by a factor of$\sqrt{10{,}000} = 100$.

Derivation: Coding Capacity

Each odorant activates a unique combination of receptor types, creating a combinatorial code. With ~400 functional receptor types in humans, the theoretical number of distinct combinations is:

$$N_{\text{codes}} = 2^{400} \approx 10^{120}$$

This number is absurdly large (more than the number of atoms in the universe!). In practice, each odorant activates approximately 10–50 receptor types out of 400. The number of possible patterns activating $k$ out of $n = 400$ receptors is:

$$\binom{400}{k} = \frac{400!}{k!(400-k)!}$$

For $k = 30$: $\binom{400}{30} \approx 10^{42}$ distinct patterns. Even accounting for noise and limited discriminability, Bushdid et al. (2014) estimated that humans can discriminate at least $10^{12}$ (one trillion) distinct odours.

The information capacity per sniff can be estimated as:

$$I = \log_2(N_{\text{distinguishable}}) \approx \log_2(10^{12}) \approx 40 \; \text{bits}$$

However, practical information transmission is limited by neural noise and cognitive processing to approximately 10–15 bits per sniff for identification tasks. This is still impressive: it means the olfactory system can identify roughly $2^{12} \approx 4,000$odour objects reliably.

Derivation: Ion Channel Mechanisms (Salt & Sour)

Salt (NaCl): Na$^+$ ions enter taste cells directly through epithelial sodium channels (ENaC). The current is:

$$I_{\text{Na}} = N \cdot \gamma_{\text{ENaC}} \cdot P_{\text{open}} \cdot (V_m - E_{\text{Na}})$$

where $\gamma_{\text{ENaC}} \approx 5$ pS. The response is proportional to extracellular [Na$^+$], making this a simple concentration sensor. This is why salt taste intensity scales almost linearly with NaCl concentration.

Sour (acid): H$^+$ ions block inwardly rectifying K$^+$ channels (and also permeate through specific proton channels like Otop1). The depolarisation arises from:

$$V_m \approx \frac{g_K E_K + g_{\text{other}} E_{\text{other}} - g_K^{\text{blocked}} E_K}{g_K - g_K^{\text{blocked}} + g_{\text{other}}}$$

As H$^+$ blocks K$^+$ channels, $g_K$ decreases, shifting $V_m$ positive and causing depolarisation. The relationship between pH and perceived sourness is approximately:

$$\psi_{\text{sour}} \propto [\text{H}^+]^{0.85} = 10^{-0.85 \cdot \text{pH}}$$

The exponent less than 1 indicates a compressive relationship: each unit drop in pH produces a diminishing increment in perceived sourness.

Taste Receptor Cell Types and Labelled Lines

Each taste receptor cell in a taste bud expresses receptors for only one taste quality. This creates a labelled-line coding scheme where the identity of the active cell specifies the taste quality, regardless of the activity pattern. The five receptor cell types are:

• • Type I cells: Glial-like support cells, may contribute to salt taste via ENaC
• • Type II cells: Express T1R or T2R GPCRs for sweet, bitter, or umami. Each cell expresses only ONE taste quality.
• • Type III cells: Sour-sensing cells expressing Otop1 proton channel. Also respond to carbonation (CO$_2$ via carbonic anhydrase).

Each taste bud contains ~50–100 cells, with a turnover time of ~10–14 days. New cells must be correctly wired to maintain taste coding — a remarkable feat of neural plasticity.

The number of taste buds varies enormously between individuals: from ~2,000 to ~10,000. "Supertasters" with high density of fungiform papillae experience taste more intensely, especially bitterness (measured by sensitivity to PROP/PTC compounds, which is genetically determined by the TAS2R38 gene).

Derivation: GPCR Mechanisms (Sweet, Bitter, Umami)

Sweet, bitter, and umami tastes share a common intracellular pathway. The tastant binds to a GPCR (T1R2/T1R3 for sweet, T2R family for bitter, T1R1/T1R3 for umami), activating gustducin (a G-protein), which activates phospholipase C$\beta$2 (PLC$\beta$2):

$$\text{Tastant} + \text{GPCR} \to G_{\text{gust}} \to \text{PLC}\beta_2 \to \text{IP}_3 \to \text{Ca}^{2+} \to \text{TRPM5}$$

IP$_3$ releases Ca$^{2+}$ from the ER, which opens TRPM5 (transient receptor potential channel M5), a non-selective cation channel. The current through TRPM5 depends on intracellular Ca$^{2+}$:

$$I_{\text{TRPM5}} = I_{\max} \cdot \frac{[\text{Ca}^{2+}]_i^n}{K_d^n + [\text{Ca}^{2+}]_i^n}$$

The depolarisation triggers ATP release through CALHM1 channels, which excites gustatory afferent nerve fibres.

Derivation: Weber-Fechner Law for Taste Intensity

Psychophysical studies of taste intensity perception follow the Weber-Fechner law. If the just-noticeable difference (JND) in stimulus concentration is proportional to the stimulus:

$$\frac{\Delta S}{S} = k_W \quad \text{(Weber's law)}$$

where $k_W$ is the Weber fraction (constant). Integrating from threshold$S_0$ to stimulus $S$:

$$\psi = \int_{S_0}^{S} \frac{dS'}{k_W S'} = \frac{1}{k_W} \ln\!\left(\frac{S}{S_0}\right)$$

$$\boxed{\psi = k \cdot \ln\!\left(\frac{S}{S_0}\right) \quad \text{(Fechner's law)}}$$

where $\psi$ is the perceived intensity. This logarithmic relationship holds reasonably well for salt and sour over moderate concentration ranges. Weber fractions for taste are typically $k_W \approx 0.1$–$0.3$ (compared to ~0.01 for audition), meaning taste discrimination is relatively coarse.

Stevens (1957) proposed a more general power law: $\psi = k \cdot (S - S_0)^\beta$where $\beta \approx 0.4$–$1.3$ for different taste qualities.

Derivation: Nasal Airflow and Odorant Transport

During a sniff, air is drawn through the nasal passages at a flow rate of$Q \approx 100$–$500$ mL/s. The nasal cavity has a complex geometry with turbinates that create narrow passages (cross-section $A \approx 1$ cm$^2$). The mean velocity is:

$$v = \frac{Q}{A} \approx \frac{200 \; \text{cm}^3/\text{s}}{1 \; \text{cm}^2} = 200 \; \text{cm/s} = 2 \; \text{m/s}$$

The Reynolds number characterises the flow regime:

$$\text{Re} = \frac{\rho v D}{\mu} = \frac{1.2 \times 2.0 \times 0.01}{1.8 \times 10^{-5}} \approx 1300$$

where $D \approx 1$ cm is the hydraulic diameter. This puts the flow in the transitional regime (200 < Re < 2000): mostly laminar but with instabilities near constrictions. The turbinates enhance odorant deposition by creating secondary vortices that push air toward the olfactory cleft.

Odorant molecules must diffuse through the ~40 $\mu$m mucus layer to reach receptors. The diffusion time is:

$$\tau_{\text{diff}} = \frac{h^2}{2D_{\text{mucus}}} = \frac{(40 \times 10^{-4})^2}{2 \times 10^{-6}} \approx 8 \; \text{ms}$$

where $D_{\text{mucus}} \approx 10^{-6}$ cm$^2$/s for small odorant molecules. Odorant-binding proteins (OBPs) in the mucus act as shuttles, increasing effective diffusivity for hydrophobic odorants.

Derivation: Optimal Sniff Rate

Active sniffing occurs at ~4–8 Hz (typically ~5 Hz) in alert animals. This frequency reflects a trade-off between two competing demands:

Sampling rate: Higher sniff rate provides more temporal information about fluctuating odour plumes. Information rate increases with sniff rate $f_s$:

$$I_{\text{sample}} \propto f_s$$

Adaptation cost: The ORN response adapts with time constant $\tau_{\text{adapt}} \approx 100$ ms. If the sniff cycle is shorter than recovery time, the response diminishes. The effective signal per sniff is:

$$R_{\text{eff}} \propto 1 - \exp(-1/(f_s \tau_{\text{adapt}}))$$

The total information rate $I_{\text{total}} = f_s \times R_{\text{eff}}$ is optimised at:

$$f_s^* \approx \frac{1}{\tau_{\text{adapt}}} \approx \frac{1}{0.2 \; \text{s}} = 5 \; \text{Hz}$$

This prediction matches the observed optimal sniff frequency remarkably well.

Electronic Noses and Artificial Taste Sensors

Electronic noses use arrays of chemical sensors that mimic the combinatorial coding of the olfactory system. Each sensor in the array has partial selectivity (like each receptor type), and pattern recognition algorithms classify the combined response. Common sensor types include:

• • Metal oxide semiconductors: Conductance changes upon gas adsorption: $\Delta G / G_0 = k \cdot [O]^\alpha$
• • Conducting polymers: Swelling changes resistance: $\Delta R / R_0 \propto$ partition coefficient $\times$ [odorant]
• • Quartz crystal microbalance: Mass loading shifts resonant frequency: $\Delta f = -2f_0^2 \Delta m / (A\sqrt{\mu\rho})$

Applications include food quality monitoring, medical breath analysis (disease biomarkers), environmental monitoring, and explosive detection.

Clinical Anosmia and Diagnostic Tools

Anosmia (loss of smell) affects ~5% of the population and can result from viral infection, head trauma, neurodegenerative disease, or congenital absence. COVID-19 caused widespread anosmia through infection of sustentacular cells in the olfactory epithelium.

Olfactory testing uses standardised tests such as the University of Pennsylvania Smell Identification Test (UPSIT), which presents 40 microencapsulated odorants. The score follows a roughly normal distribution: mean ~35/40 for young adults, declining with age. A score below 19/40 indicates anosmia; 20–33 indicates hyposmia.

Olfactory dysfunction is an early biomarker for Parkinson's disease and Alzheimer's disease, often appearing years before motor or cognitive symptoms. The mechanism involves early accumulation of alpha-synuclein (Parkinson's) or tau (Alzheimer's) in the olfactory bulb and anterior olfactory nucleus.

Flavour Science

What we call "flavour" is not just taste — it is a multimodal integration of taste, retronasal olfaction (odorants reaching the olfactory epithelium from the back of the mouth during chewing), trigeminal sensation (spiciness from capsaicin, cooling from menthol), texture, temperature, and even sound (the crunch of a crisp).

The contribution of olfaction to flavour can be quantified: when subjects pinch their nose, their ability to identify foods drops by ~80%. This is because most of the complexity in food perception comes from the hundreds of volatile compounds detected retronasally, not from the five basic tastes.

The orthonasal/retronasal asymmetry is notable: the same odorant can evoke different percepts depending on the route. Orthonasal (sniffing) activates a "source identification" pathway, while retronasal activates a "flavour evaluation" pathway with different cortical representations.

Odorant Structure-Activity Relationships

The relationship between molecular structure and perceived odour remains one of the great unsolved problems in sensory science. Some general principles exist:

• • Molecular shape: The "lock and key" model predicts that odorants bind based on shape complementarity with the receptor binding pocket. Enantiomers (mirror-image molecules) often smell different: (R)-limonene smells of orange, (S)-limonene of lemon.
• • Functional groups: Thiols (-SH) tend to smell sulphurous, esters fruity, aldehydes pungent. But exceptions abound.
• • Molecular vibration theory: Luca Turin proposed that olfactory receptors detect molecular vibration frequencies via inelastic electron tunnelling. The predicted tunnelling current is $I \propto \exp(-\beta d) \cdot \delta(\Delta E - \hbar\omega_{\text{vib}})$where $\beta$ is the tunnelling decay constant, $d$ is the barrier width, and the delta function selects for specific vibrational quanta. This remains controversial.