End-to-End Acoustic Communication in Plants

• The paper formalizes plant acoustic signaling by integrating biophysical emission processes with digital communications principles like modulation, channel estimation, and error correction.
• It models the entire communication chain—from cavitation-induced ultrasonic clicks and substrate vibrations to mechanosensitive channel responses—using simulation-ready frameworks.
• The work has practical implications for precision irrigation and bio-inspired sensor networks by enabling non-invasive, quantitative plant stress detection.

End-to-end acoustic communication frameworks for plants formalize phytoacoustic signal processing using canonical information and communication theory constructs—transmitter, channel, and receiver—enabling quantitative modeling from physical stimulus to biological response. Such frameworks have been systematically developed in recent works, most notably in "An Acoustic Communication Model in Plants" (Merdan et al., 30 Nov 2025) and the survey "Information and Communication Theoretical Foundations of the Internet of Plants" (Kilic et al., 10 Sep 2025). These frameworks integrate biophysical emission mechanisms, environmental propagation, cellular signal transduction, and downstream physiological effects into tractable, simulation-ready models, facilitating direct application of digital communications concepts (e.g., modulation, channel capacity, error correction) to plant signaling.

1. Biological and Physical Basis of Plant Acoustic Communication

Plant acoustic communication arises from distinct physical and physiological origins depending on modality (e.g., airborne or substrate-borne sound). Two principal pathways have been characterized:

• Emission:

In xylem-mediated signaling, cavitation events (nucleation/collapse of water columns under tension) act as impulsive broadband transmitters, producing ultrasonic clicks (20–200 kHz). The click rate encodes stress conditions such as drought or mechanical injury (Kilic et al., 10 Sep 2025). Alternatively, in substrate-root signaling, flowing water or mechanical perturbations generate low-frequency (∼200 Hz) pressure oscillations in soil, stimulating root mechanoreceptors (Merdan et al., 30 Nov 2025).

• Detection:

Mechanosensitive (MS) ion channels embedded in plant cell membranes (notably MCA2 in root epidermal cells) function as primary receivers, opening in response to mechanical stress and converting acoustic energy into ionic current, triggering downstream biochemical cascades (Merdan et al., 30 Nov 2025, Kilic et al., 10 Sep 2025).

• Key Structures:

Xylem vessels, phloem, and parenchyma serve as emission sites and potential waveguides. Trichomes, root hairs, and petal surfaces may enhance acoustic coupling at the receiver interface.

2. Transmitter Design, Signal Modeling, and Encoding

Transmitter models are constructed by characterizing the biophysical origin of the acoustic waveform and its information content:

• Resonant Vessel Model:

Each cavitation event is modeled by a damped sinusoid:

$$p_s(t) = A\, e^{-t/\tau_s}\, \sin(2\pi f_0 t)\, H(t)$$

where $A$ is peak overpressure, $\tau_s$ is the damping time, $f_0 = \frac{1}{2L}v_l$ is the vessel resonance, and $H(t)$ is the unit step (Kilic et al., 10 Sep 2025). Typical parameters: $A \approx 0.1$–$1$ Pa, $\tau_s \approx 0.5$ ms, $f_0 \approx 40$–$80$ kHz.

• Modulation:
  • On-Off Keying (OOK): information is encoded in the presence/absence of a click per time slot.
  • Pulse Position Modulation (PPM): the time index of a click is shifted to encode multiple bits per symbol (Kilic et al., 10 Sep 2025).
• Soil Water Flow Model:

Broadband pressure oscillations in soil, centered at $f_0=200$ Hz, are modeled as summed viscoelastic damped sinusoids (Kelvin–Voigt/Biot model) with amplitude $$A_s \sim \mathcal{N}(20\,\mu\text{Pa},\,1\,\mu\text{Pa})$$ (Merdan et al., 30 Nov 2025).

The transmitted waveform $x(t)$ is a sum over $N$ symbols:

$x(t) = \sum_{k=0}^{N-1} b_k\, p_s(t - kT_s)$

where $b_k \in \{0,1\}$ are modulation symbols.

3. Channel Propagation and Noise Modeling

• Airborne and Tissue Channels:

Impulse response in air or tissue is given by:

$$h(t) = \frac{\kappa}{r}\, e^{-\alpha(f) r}\, \delta\!\left( t - \frac{r}{c} \right)$$

where $\alpha(f)$ is absorption ($0.1$–$2$ dB/m in air at $20$–$100$ kHz, $>10$ dB/m in soil above $20$ kHz), $c$ is sound speed, and $r$ is distance (Kilic et al., 10 Sep 2025). Dispersion is negligible in air and low frequency modes; higher modes may arise in xylem tissue. Substrate-based propagation in soil is modeled using a low-frequency viscoelastic Kelvin–Voigt framework, parameterized by bulk density, viscosity, and shear modulus for clay soils (Merdan et al., 30 Nov 2025).

• Noise Sources:
  • Environmental noise: wind, rain, insect signals (modeled as colored Gaussian or 1/f pink noise in soils).
  • Multi-source interference: superposition of clicks or oscillations from multiple plants.
  • Thermal noise is negligible at ultrasonic frequencies.
• Path Loss and Channel Estimation:

Path loss combines geometric spreading and absorption:

$L(f,\text{dB}) = 20 \log_{10}(r) + \alpha(f)\, r$

In practical setups, channel impulse response is empirically estimated via time-of-arrival measurements at multiple distances (Kilic et al., 10 Sep 2025).

4. Receiver Modeling and Signal Processing

The receiver block, whether biological or engineered, applies signal processing strategies informed by both plant physiology and classical communications principles.

• Biological Receiver:

On the plant side, impinging pressure at root surfaces is transduced into electrical signals by MS channels (e.g., MCA2), whose open-probability $P_0(\sigma, V)$ is a nonlinear function of membrane stress and potential:

$$P_0(V,\sigma) = l\,[1+e^{(V_h-V)/k_V}]^{-1}\,[1+e^{(\sigma_h-\sigma)/k_\sigma}]^{-1}$$

Ca$^{2+}$ current through an open channel follows Nernst–Planck kinetics and drives a cytosolic Ca$^{2+}$ rise, quantified by a detailed ODE system, with Ca$^{2+}$, ROS, CPK29 kinase, PIN2 phosphorylation, and ultimately differential cell expansion (root bending) as cascade stages (Merdan et al., 30 Nov 2025).

• Engineered Signal Chain:

For digital monitoring, an acoustic sensor (ultrasonic microphone or hydrophone) detects $y(t) = (x * h)(t) + n(t)$, followed by: 1. Bandpass filtering ($f_1$–$f_2$; e.g., $20$–$200$ kHz). 2. Matched filtering to the canonical $p_s(t)$ waveform. 3. Envelope or energy detection in symbol slots ($E_k$). 4. Threshold detection ($\hat{b}_k$). 5. PPM demodulation (slot energy maximization) (Kilic et al., 10 Sep 2025).

5. End-to-End Implementation and Simulation

A full plant-to-plant or plant-to-sensor communication link is implemented as follows:

• Transmission Induction:

Mechanical or osmotic (drought) stress is applied to elicit cavitation or controlled water flow, generating naturalistic acoustic emission (Kilic et al., 10 Sep 2025, Merdan et al., 30 Nov 2025).

• Experimental Setups:
  • Laser Doppler vibrometry for tissue-borne waves.
  • Anechoic chambers and particle-velocity microphones for airborne clicks.
  • Contact piezo or hydrophone sensors for substrate detection at roots (Kilic et al., 10 Sep 2025).
  • Soil-embedded sound sources (patch speakers) for substrate flow studies (Merdan et al., 30 Nov 2025).
• Parameters and Decision Metrics:
  • A $200$ Hz, $20\,\mu$Pa stimulus elevates cytosolic Ca$^{2+}$ from $150$ nM to $230 \pm 10$ nM within $50$ s.
  • Activated PIN2 ratio, $APR = P_a(t_f)/P_a(t_i)$, is used for symbol detection: $APR > 5$ interprets a "1," else "0."
  • Monte Carlo performance: BER near zero above $20\,\mu$Pa amplitude or decision windows $T_\text{bit} \gtrsim 100$ s; BER rises steeply for frequencies above $300$ Hz (acoustic "tuning") (Merdan et al., 30 Nov 2025).
• Blueprint Steps (Editor’s term):

Steps include emission induction, waveform and channel characterization, receiver calibration and filtering, noise measurement, SNR/capacity estimation, and real-time detection, with extension to adaptive symbol intervals and simple error correction if required (Kilic et al., 10 Sep 2025).

6. Information-Theoretic Analysis

Plant acoustic channels permit direct application of information and communication theoretic metrics:

• SNR:

$$\mathrm{SNR} = \frac{\int_{f_1}^{f_2} |X(f)H(f)|^2\,df}{\int_{f_1}^{f_2} N(f)\,df}$$

In practical settings, $A$ (emission amplitude), $N_0$ (noise spectral density), $r$ (distance), and $\alpha$ (attenuation) determine SNR. Typical SNRs for 0.1–1 Pa, tens of kHz frequencies, and meter-scale distances can be computed for design (Kilic et al., 10 Sep 2025).

• Capacity Bound:

$$C = \int_{f_1}^{f_2} \log_2\left(1 + \frac{|X(f)H(f)|^2}{N(f)}\right)\,df$$

For flat channel/noise over $B = f_2 - f_1$, $C \approx B \log_2(1+\mathrm{SNR})$ (Kilic et al., 10 Sep 2025).

• Error Rates:

Bit error rates (BERs) derived via Monte Carlo simulation under realistic noise and biological response assumptions enable design tradeoff assessment (Merdan et al., 30 Nov 2025).

7. Applications, Open Challenges, and Future Directions

• Applications:
  • Precision irrigation and plant-health monitoring via root-sensitive acoustic signaling and detection.
  • Non-invasive plant stress sensing using ultrasonic or substrate-based acoustic signatures.
  • Bio-inspired soil communication elements ("acoustic routers") in distributed sensor networks.
  • Research on acoustic memory and breeding for enhanced sensitivity (Merdan et al., 30 Nov 2025, Kilic et al., 10 Sep 2025).
• Challenges:
  • Achieving sufficient SNR in noise-rich (soil and field) environments.
  • Decoding biological variability and complexity in plant transduction pathways.
  • Integration with other modalities—chemical, electrical, mycorrhizal—to construct holistic Internet of Plants (IoP) models (Kilic et al., 10 Sep 2025).
• Future Directions:

The plant acoustic communications paradigm serves as a test case for molecular and biophysical communication theory, and provides a physical substrate for ecological and technological networking, with implications for climate resilience and bio-hybrid systems (Kilic et al., 10 Sep 2025, Merdan et al., 30 Nov 2025). This suggests ongoing development will target both fundamental understanding and agritech deployment.