Module 5

Sensory Systems

Slit sensilla, lyriform organs, trichobothria, and web vibration analysis — sensing the world through strain and airflow

5.1 Slit Sensilla: Strain Sensors in the Exoskeleton

Slit sensilla are mechanoreceptors unique to arachnids — no other animal group possesses them. Each slit sensillum is a narrow crack-like opening in the exoskeleton, typically \(\sim 1 \;\mu\text{m}\) wide and \(8{-}200 \;\mu\text{m}\) long, covered by a thin cuticular membrane. A bipolar sensory neuron attaches to the membrane and fires when the slit deforms.

Slit sensilla detect:

• Substrate vibrations transmitted through the legs
• Hemolymph pressure changes (proprioception)
• Body deformation during locomotion and prey handling
• Web vibrations propagated through silk threads

Strain Amplification

The slit geometry creates a strain concentrator. The amplification factor \(G\) relates the strain at the slit membrane to the bulk strain in the surrounding exoskeleton:

\( G = \frac{\varepsilon_{\text{slit}}}{\varepsilon_{\text{substrate}}} \approx \frac{L}{w} \)

where \(L\) is the slit length and \(w\) is the slit width. For a typical slit (\(L = 100 \;\mu\text{m}\), \(w = 1 \;\mu\text{m}\)):

\( G \approx \frac{100}{1} = 100\times \)

This means a bulk strain of \(10^{-6}\) (one microstrain) produces a local strain of\(10^{-4}\) at the slit membrane — well within the neuron's detection threshold.

Resonant Frequency

Each slit has a natural resonant frequency determined by its geometry and the membrane's mechanical properties:

\( f_{\text{res}} = \frac{1}{2L}\sqrt{\frac{T_{\text{membrane}}}{\rho_{\text{membrane}} \cdot t}} \)

where \(T_{\text{membrane}}\) is the membrane tension, \(\rho_{\text{membrane}}\)is the density, and \(t\) is the membrane thickness. Typical resonant frequencies range from 100 Hz to 3 kHz, well matched to the frequency content of prey vibrations.

5.2 Lyriform Organs: Biological Spectrometers

Lyriform organs are arrays of parallel slit sensilla arranged near leg joints, typically containing 5–30 slits of different lengths. The name derives from their lyre-shaped appearance. Found predominantly near the tibia-metatarsus joint (the most vibration-sensitive location on the leg).

The critical insight: because each slit has a different length, it has a different resonant frequency. The array therefore functions as a frequency analyser — a biological spectrometer that decomposes incoming vibrations into their frequency components, analogous to the mammalian cochlea.

Frequency Decomposition

For an array of \(N\) slits with lengths \(L_1 < L_2 < \ldots < L_N\), each slit \(n\) responds maximally at:

\( f_n = \frac{c_{\text{membrane}}}{2 L_n} \)

where \(c_{\text{membrane}}\) is the wave speed in the slit membrane. The frequency response of each slit follows a Lorentzian (damped resonance):

\( R_n(f) = \frac{A_0}{\sqrt{(f^2 - f_n^2)^2 + (\gamma f)^2}} \)

where \(\gamma\) is the damping coefficient. A typical lyriform organ with slits ranging from 10 to 200 \(\mu\)m covers a frequency range of roughly 50 Hz to 5 kHz, spanning the full spectrum of biologically relevant vibrations (prey struggles, courtship signals, predator footsteps).

Comparison to Mammalian Cochlea

The cochlea achieves frequency decomposition through a tapered basilar membrane of varying width and stiffness. The lyriform organ achieves the same result through discrete slits of varying length. Both are tonotopically organised — a stunning case of convergent evolution between arachnids and mammals.

5.3 Trichobothria: Air Current Sensors

Trichobothria are ultra-sensitive hair-like sensors on spider legs that detect airflow disturbances caused by approaching prey (e.g., flying insects) or predators. Each trichobothrium is a fine hair (\(L \approx 0.1{-}1\) mm,\(d \approx 5{-}10 \;\mu\text{m}\)) mounted in a flexible socket with a bipolar neuron.

Sensitivity is extraordinary: trichobothria can detect air velocities as low as 0.1 mm/s — below the threshold of human perception. The hair deflects by as little as 0.01° in response to faint air currents.

Mechanics of Hair Deflection

The drag force on the trichobothrium hair (modelled as a cylinder in low-Reynolds-number flow) follows the Stokes drag formula:

\( F_{\text{drag}} = \frac{4\pi \mu L v}{\ln(2L/d)} \)

• \(\mu \approx 1.8 \times 10^{-5}\) Pa\(\cdot\)s: dynamic viscosity of air
• \(L\): hair length
• \(v\): air velocity
• \(d\): hair diameter
• \(\ln(2L/d)\): logarithmic correction for slender body (typically \(\approx 4{-}6\))

The hair deflects against a torsional restoring spring at the socket. The angular deflection:

\( \theta = \frac{F_{\text{drag}} \cdot L/2}{k_{\text{torsion}}} \)

The natural frequency of oscillation:

\( f_0 = \frac{1}{2\pi}\sqrt{\frac{k_{\text{torsion}}}{I}} \)

where \(I = \frac{1}{3}\rho_{\text{hair}} \cdot \frac{\pi d^2}{4} \cdot L^3\) is the moment of inertia of the hair about its base. Typical natural frequencies are 40–600 Hz, well matched to the wingbeat frequencies of flying insects (prey).

Figure 5.1: Three major mechanosensory organs. Left: slit sensillum cross-section showing strain amplification. Centre: lyriform organ with parallel slits of varying length for frequency decomposition. Right: trichobothrium deflected by airflow.

5.4 Web Vibration Analysis

Web-building spiders can identify prey type, size, and location from web vibrations alone — all without vision. The web acts as an extended sensory organ, transmitting vibrational information to the spider's legs via slit sensilla and lyriform organs.

Wave Propagation in Silk

Transverse waves propagate along silk threads at a velocity determined by the tension and linear mass density:

\( v = \sqrt{\frac{T}{\rho_{\text{linear}}}} = \sqrt{\frac{T}{\rho \cdot A}} \)

• \(T\): silk thread tension (typically 1–100 mN depending on thread type)
• \(\rho_{\text{linear}}\): mass per unit length (\(\sim 10^{-6}\) kg/m)
• \(\rho \approx 1300\) kg/m\(^3\): silk density
• \(A\): cross-sectional area of thread

Wave speeds in spider silk range from 10 to 500 m/s depending on silk type and pre-tension:

Radial Threads (Dragline Silk)

High tension, high stiffness. Wave speed \(\sim 100{-}500\) m/s. Primarily transmit longitudinal waves. Act as high-speed signal pathways.

Capture Spiral (Viscid Silk)

Lower tension, highly extensible. Wave speed \(\sim 10{-}50\) m/s. Better at transmitting transverse vibrations. Acts as the prey-detection zone.

Prey Identification by Frequency

Different prey produce characteristic vibration spectra:

• Flies: high-frequency buzzing, 100–300 Hz, intermittent bursts
• Beetles: low-frequency, 20–80 Hz, sustained struggling
• Wind/debris: broadband, low amplitude, no characteristic frequency
• Male spider courtship: species-specific rhythmic patterns, 5–50 Hz

The spider triangulates prey position using arrival time differences between legs (resolution \(\sim 1{-}2\) ms). The frequency-dependent wave speed in different silk types creates a natural “filter bank” that aids in source identification.

5.45 Vibration Source Localisation

A web-building spider can pinpoint prey location with remarkable accuracy, typically within 1–2 cm on a web spanning 30+ cm. The mechanism relies on inter-leg time differences (ILTDs) — analogous to the interaural time differences used by vertebrates for sound localisation.

Time-Difference Localisation

For a vibration originating at position \(\mathbf{r}_{\text{prey}}\) on the web, the arrival time at leg \(i\) (positioned at \(\mathbf{r}_i\)) is:

\( t_i = \frac{|\mathbf{r}_{\text{prey}} - \mathbf{r}_i|}{v_{\text{web}}} + t_0 \)

The spider compares arrival times at different legs. With 8 legs positioned around the web hub, the spider has up to \(\binom{8}{2} = 28\) pairwise time differences. The minimum detectable time difference is approximately \(\Delta t_{\min} \approx 0.5{-}2\) ms, limited by neural conduction velocity and synaptic jitter.

For a wave speed of \(v \approx 200\) m/s (radial thread) and leg separation of\(\Delta r \approx 5\) mm, the maximum time difference is:

\( \Delta t_{\max} = \frac{\Delta r}{v} = \frac{5 \times 10^{-3}}{200} = 25 \;\mu\text{s} \)

This is far shorter than the neural resolution. However, the spider compensates by using amplitude differences between legs (which are much larger due to attenuation with distance) and the frequency-dependent propagation of different silk types.

Frequency-Dependent Attenuation

Vibrations attenuate as they propagate through the web. Higher frequencies attenuate faster, following an exponential decay:

\( A(x, f) = A_0 \cdot e^{-\alpha(f) \cdot x}, \quad \alpha(f) = \alpha_0 \sqrt{f} \)

where \(\alpha_0 \approx 0.01{-}0.1\) m\(^{-1}\)Hz\(^{-1/2}\). This means a spider at the hub receives a frequency spectrum that encodes the distance to the prey: nearby prey produce high-frequency signals, while distant prey signals are dominated by low frequencies (natural low-pass filtering).

5.5 Chemoreception: Tasting with Feet

Spiders possess tarsal contact chemoreceptors — they literally taste whatever they walk on. These sensors are located on the tips of the legs (tarsi and pretarsi) and consist of hollow setae (hairs) with pores at the tip, through which molecules in contact with the surface diffuse to reach chemosensory neurons.

Prey Recognition

Contact chemoreceptors help distinguish prey from non-food items after capture. Spiders will reject distasteful prey (e.g., ants with formic acid) upon first contact with the chelicerae.

Pheromone Detection

Male spiders detect female pheromones deposited on silk draglines and web structures. The male follows the chemical trail to locate a receptive female, often tapping the silk with his palps to “read” the pheromone signature.

Chemical Sensing Mechanisms

The chemosensory setae contain multiple receptor neurons, each tuned to different molecular classes. The response follows a Hill equation for cooperative binding:

\( R = R_{\max} \cdot \frac{[C]^n}{K_d^n + [C]^n} \)

• \(R\): neural response (firing rate)
• \([C]\): concentration of the chemical stimulus
• \(K_d\): dissociation constant (sensitivity)
• \(n\): Hill coefficient (cooperativity, typically 1–3)

Bolas spiders (Mastophora) exploit chemoreception in a remarkable way: they release volatile chemicals that mimic moth pheromones, luring male moths toward the spider. The spider then swings a sticky silk “bolas” to capture the attracted moth — a case of aggressive chemical mimicry.

5.55 Multi-Modal Sensory Integration

A spider's brain (supraoesophageal ganglion) must integrate information from hundreds of mechanosensors simultaneously. A single leg contains approximately:

~300

Slit sensilla

5–15

Lyriform organs

~100

Trichobothria

~50

Chemoreceptors

Across all 8 legs and the pedipalps, a spider processes signals from ~3,500+ individual mechanosensors — an extraordinary feat for a brain with only ~100,000–600,000 neurons (compared to ~86 billion in humans).

The central nervous system uses corollary discharge to distinguish self-generated vibrations (from its own movements) from external signals. During locomotion, the spider's brain sends copies of motor commands to the sensory processing centres, allowing it to “subtract” its own movements and remain sensitive to prey signals even while walking.

This sensory integration enables behaviours of remarkable sophistication: web-building spiders can simultaneously monitor web tension (slit sensilla), detect prey vibrations (lyriform organs), sense approaching predators via air currents (trichobothria), and chemically assess prey quality (tarsal chemoreceptors) — all with a brain smaller than a pinhead.

5.6 Computational Analysis

Sensory Organ Physics

Slit Sensillum, Lyriform Organ, and Trichobothrium Analysis

Python

script.py147 lines

import numpy as np
import matplotlib
matplotlib.use('Agg')
import matplotlib.pyplot as plt

fig, axes = plt.subplots(2, 2, figsize=(14, 11))
fig.patch.set_facecolor('#0a0a0a')
for ax in axes.flat:
    ax.set_facecolor('#111111')
    ax.tick_params(colors='#cccccc')
    for spine in ax.spines.values():
        spine.set_color('#444444')

# === 1. Slit Sensillum Strain Amplification ===
slit_lengths = np.array([10, 25, 50, 100, 150, 200])  # um
slit_width = 1.0  # um
G = slit_lengths / slit_width

# Frequency response of each slit (simple model)
c_membrane = 5.0  # effective wave speed in membrane (m/s)
f_res = c_membrane / (2 * slit_lengths * 1e-6)  # Hz

colors_slit = ['#ef4444', '#f97316', '#eab308', '#22d3ee', '#a855f7', '#4ade80']
freqs = np.linspace(10, 5000, 1000)

for i, (L, fr, col) in enumerate(zip(slit_lengths, f_res, colors_slit)):
    gamma = fr * 0.15  # damping
    response = 1.0 / np.sqrt((freqs**2 - fr**2)**2 + (gamma * freqs)**2)
    response /= np.max(response)
    axes[0,0].plot(freqs, response * (L / slit_width), color=col, linewidth=1.5,
                   label=f'L={L} um, G={L/slit_width:.0f}x, f_r={fr:.0f} Hz')

axes[0,0].set_xlabel('Frequency (Hz)', color='#cccccc', fontsize=11)
axes[0,0].set_ylabel('Amplified response (a.u.)', color='#cccccc', fontsize=11)
axes[0,0].set_title('Slit Sensillum: Strain Amplification vs Frequency',
                     color='#c4b5fd', fontsize=13, fontweight='bold')
axes[0,0].legend(fontsize=8, facecolor='#1a1a2e', edgecolor='#555', labelcolor='#cccccc')
axes[0,0].set_xlim(0, 4000)

# === 2. Lyriform Organ Frequency Decomposition ===
n_slits = 12
L_array = np.linspace(15, 180, n_slits)  # um
f_array = c_membrane / (2 * L_array * 1e-6)  # resonant frequencies

# Input signal: composite vibration (fly at 200 Hz + beetle at 50 Hz)
f_fly = 200.0
f_beetle = 50.0
input_spectrum = np.zeros_like(freqs)
input_spectrum += 0.8 * np.exp(-((freqs - f_fly) / 20)**2)
input_spectrum += 1.0 * np.exp(-((freqs - f_beetle) / 10)**2)

axes[0,1].fill_between(freqs, input_spectrum, alpha=0.2, color='white', label='Input vibration')
axes[0,1].plot(freqs, input_spectrum, color='white', linewidth=1, alpha=0.5)

cmap = plt.cm.plasma
for i, (L, fr) in enumerate(zip(L_array, f_array)):
    gamma = fr * 0.12
    response = 1.0 / np.sqrt((freqs**2 - fr**2)**2 + (gamma * freqs)**2)
    response /= np.max(response)
    output = response * input_spectrum
    col = cmap(i / n_slits)
    axes[0,1].fill_between(freqs, output, alpha=0.15, color=col)
    axes[0,1].plot(freqs, output, color=col, linewidth=1.2)
    # Mark resonant frequency
    axes[0,1].axvline(x=fr, color=col, linestyle=':', linewidth=0.6, alpha=0.5)

axes[0,1].set_xlabel('Frequency (Hz)', color='#cccccc', fontsize=11)
axes[0,1].set_ylabel('Response amplitude', color='#cccccc', fontsize=11)
axes[0,1].set_title('Lyriform Organ: Frequency Decomposition',
                     color='#c4b5fd', fontsize=13, fontweight='bold')
axes[0,1].set_xlim(0, 2000)
axes[0,1].annotate('Beetle\n(50 Hz)', xy=(50, 0.9), color='#fbbf24', fontsize=10, ha='center')
axes[0,1].annotate('Fly\n(200 Hz)', xy=(200, 0.7), color='#fbbf24', fontsize=10, ha='center')

# === 3. Trichobothrium Sensitivity ===
mu_air = 1.8e-5   # Pa.s
hair_lengths = np.array([0.1, 0.2, 0.5, 0.8, 1.0]) * 1e-3  # m
hair_d = 7e-6      # m

v_air = np.linspace(0.0001, 0.01, 500)  # m/s (0.1 to 10 mm/s)

for L, col in zip(hair_lengths, ['#22d3ee', '#a855f7', '#f97316', '#ef4444', '#4ade80']):
    ln_factor = np.log(2 * L / hair_d)
    F_drag = 4 * np.pi * mu_air * L * v_air / ln_factor  # N
    # Angular deflection
    k_torsion = 5e-12  # N.m/rad (very soft spring)
    theta = F_drag * L / 2 / k_torsion  # rad
    theta_deg = np.degrees(theta)
    axes[1,0].semilogy(v_air * 1000, theta_deg, color=col, linewidth=2,
                       label=f'L = {L*1000:.1f} mm')

axes[1,0].axhline(y=0.01, color='#666', linestyle='--', linewidth=1, label='Detection threshold (0.01 deg)')
axes[1,0].set_xlabel('Air velocity (mm/s)', color='#cccccc', fontsize=11)
axes[1,0].set_ylabel('Hair deflection (degrees)', color='#cccccc', fontsize=11)
axes[1,0].set_title('Trichobothrium: Deflection vs Air Velocity',
                     color='#c4b5fd', fontsize=13, fontweight='bold')
axes[1,0].legend(fontsize=9, facecolor='#1a1a2e', edgecolor='#555', labelcolor='#cccccc')
axes[1,0].set_ylim(1e-4, 100)

# === 4. Web Vibration Propagation ===
silk_types = {
    'Dragline (radial)': {'T': 50e-3, 'rho_l': 1e-6, 'color': '#ef4444'},
    'Minor ampullate': {'T': 20e-3, 'rho_l': 0.5e-6, 'color': '#f97316'},
    'Flagelliform (spiral)': {'T': 2e-3, 'rho_l': 0.3e-6, 'color': '#a855f7'},
    'Capture spiral + glue': {'T': 1e-3, 'rho_l': 0.8e-6, 'color': '#22d3ee'},
}

# Wave propagation: v = sqrt(T / rho_linear)
distances = np.linspace(0, 0.3, 500)  # metres (up to 30 cm web radius)

for name, params in silk_types.items():
    v_wave = np.sqrt(params['T'] / params['rho_l'])
    t_arrival = distances / v_wave * 1000  # ms
    axes[1,1].plot(distances * 100, t_arrival, color=params['color'], linewidth=2,
                   label=f"{name}: v={v_wave:.0f} m/s")

# Mark prey distances
for d, prey in [(5, 'Close prey'), (15, 'Mid-web'), (25, 'Web edge')]:
    axes[1,1].axvline(x=d, color='#666', linestyle=':', linewidth=0.8)
    axes[1,1].text(d+0.5, 0.05, prey, color='#999', fontsize=9, rotation=90, va='bottom')

axes[1,1].set_xlabel('Distance from prey impact (cm)', color='#cccccc', fontsize=11)
axes[1,1].set_ylabel('Signal arrival time (ms)', color='#cccccc', fontsize=11)
axes[1,1].set_title('Web Vibration Propagation: Arrival Time',
                     color='#c4b5fd', fontsize=13, fontweight='bold')
axes[1,1].legend(fontsize=9, facecolor='#1a1a2e', edgecolor='#555', labelcolor='#cccccc')

plt.tight_layout()
plt.savefig('output.png', dpi=150, bbox_inches='tight', facecolor='#0a0a0a')

print("Slit sensillum strain amplification:")
for L in slit_lengths:
    fr = c_membrane / (2 * L * 1e-6)
    print(f"  L={L} um: G={L/slit_width:.0f}x, f_res={fr:.0f} Hz")

print("\nTrichobothrium sensitivity (L=0.5 mm):")
L_test = 0.5e-3
ln_f = np.log(2*L_test/hair_d)
for v in [0.1e-3, 0.5e-3, 1e-3, 5e-3]:
    F = 4*np.pi*mu_air*L_test*v/ln_f
    th = np.degrees(F*L_test/2/5e-12)
    print(f"  v={v*1000:.1f} mm/s: F_drag={F*1e9:.2f} nN, theta={th:.3f} deg")

print("\nWeb silk wave speeds:")
for name, p in silk_types.items():
    v = np.sqrt(p['T']/p['rho_l'])
    print(f"  {name}: v = {v:.0f} m/s")

Click Run to execute the Python code

Code will be executed with Python 3 on the server

References

• Barth, F.G. (2002). A Spider's World: Senses and Behavior. Springer-Verlag, Berlin.
• Barth, F.G. (2004). Spider mechanoreceptors. Current Opinion in Neurobiology, 14(4), 415–422.
• Barth, F.G. & Libera, W. (1970). Ein Atlas der Spaltsinnesorgane von Cupiennius salei. Zeitschrift für Morphologie der Tiere, 68, 343–369.
• Humphrey, J.A.C. et al. (1993). Dynamics of arthropod filiform hairs. I. Mathematical modelling of the hair and air motions. Philosophical Transactions of the Royal Society B, 340(1294), 423–444.
• Mortimer, B. et al. (2016). Tuning the instrument: sonic properties in the spider's web. Journal of the Royal Society Interface, 13(122), 20160341.
• Fratzl, P. & Barth, F.G. (2009). Biomaterial systems for mechanosensing and actuation. Nature, 462, 442–448.
• Landolfa, M.A. & Barth, F.G. (1996). Vibrations in the orb web of the spider Nephila clavipes: cues for discrimination and orientation. Journal of Comparative Physiology A, 179(4), 493–508.
• Foelix, R.F. (2011). Biology of Spiders, 3rd edition. Oxford University Press.