Sensory Prompting in Collective Networks

• Sensory prompting is a mechanism where cells or agents respond and synchronize their actions by integrating intrinsic properties with external stimuli.
• Experimental studies using microfluidics and stochastic models demonstrate that increased ATP stimulation and cell density lower activation thresholds and enhance oscillatory coherence.
• Optimized sensory prompting leverages network connectivity to improve system sensitivity and synchrony, with implications for neurobiology, robotics, and HCI.

Sensory prompting refers to the mechanisms by which an agent (biological or artificial) is modulated or “primed” to generate, modify, or synchronize responses to external or internal stimuli. While the concept historically spans neurobiology, robotics, human-computer interaction, and artificial intelligence, research across disparate domains converges on a key principle: the interplay of intrinsic system properties and extrinsic signals, often mediated or optimized by communication or computational architectures, can dramatically shape collective and individual sensory responses.

1. Multicellular Communication and Emergence of Collective Sensory Prompting

In multicellular systems, sensory prompting is exemplified by the collective calcium signaling observed in fibroblast monolayers communicating via gap junctions (Potter et al., 2015). The underlying mechanism relies on both chemical stimulation (e.g., ATP-induced IP₃-mediated calcium release) and physical cell–cell coupling (mediated by gap junctions).

The experimental and modeling framework demonstrates that increasing ATP stimulus (represented as the IP₃ production rate, α) and increasing cell density both enhance the network’s propensity to exhibit calcium oscillations. Communication—modeled as diffusive calcium coupling with a hopping rate h = 0.01–0.04 s⁻¹—does not merely propagate signals, but actively “prompts” neighboring cells, lowering the activation threshold and synchronizing oscillatory behavior across the network.

A distinguishing feature is that cell–cell communication enables the network to operate in a critical region of parameter space where both the fraction of oscillating cells (F_N) and the inter-spike interval (ISI) distributions are modulated by both stimulus and connectivity. The network effectively multiplexes information about external stimuli and local microenvironment (neighbor connectivity), a phenomenon disrupted by introducing cancer cells that act as “defects” in the communication pathway.

2. Stochastic Modeling and Sensory Response Optimization

The application of stochastic modeling reveals that noise and cell-to-cell variability fundamentally shape the collective sensory response (Potter et al., 2015). The classical deterministic oscillatory model (adapted from Tang and Othmer) is extended to include noise, parameter heterogeneity, and explicit communication.

The model’s dynamics can be summarized by stochastic differential equations, e.g.,

$$ε\frac{dc}{dτ}= F_{\text{stimulus}}(α, x_4) - \text{NonlinearPump}(c) + \text{(Communication terms)}$$

where the communication terms are discrete diffusive couplings between neighboring cells in a lattice topology.

Key insights:

• The transition from non-oscillatory to oscillatory regimes is broadened by noise.
• Spatial correlations in ISI vanish with increased intrinsic noise and heterogeneity, indicating decentralized, variability-driven promptings.
• Enhanced cell density not only increases average oscillatory propensity but narrows the ISI distribution, yielding a more coherent ensemble signal.
• Cancer cells, by reducing gap junctional coupling, decouple regions of the network, increasing the fraction of non-oscillating cells and broadening response distributions.

These effects highlight that optimal sensory prompting in biological collectives is not purely a function of stimulus strength, but depends crucially on network connectivity and emergent variability.

3. Experimental Validation of Sensory Prompting Principles

Quantitative validation combines microfluidic stimulation of fibroblast monolayers with high-resolution fluorescence imaging (Potter et al., 2015). Controlled ATP dosing (0–200 μM) elicits single-cell calcium profiles, from which ISIs and F_N can be extracted via peak detection algorithms.

The main experimental findings are:

• F_N decreases as cell density increases at a fixed stimulus.
• ISI entropy is reduced (i.e., the distribution narrows) in denser cultures, indicating increased synchrony.
• Cross-cell ISI correlation decays rapidly with topological distance, indicating local communication is the primary driver of coordinated response.
• Introduction of cancer cells (defective communicators) raises F_N and fastens ISI entropy locally.

The concurrence between stochastic model predictions and empirical results substantiates both the mechanistic underpinnings and the critical regime positioning hypothesis.

4. Theoretical Foundation: Phase Diagram and Multiplexed Encoding

A simplified phase diagram in (α, ρ_T) space (with α the IP₃ production rate and ρ_T the cell density) delineates regions characterized by distinct fractions of oscillating cells. The system exhibits an extended “critical region” emanating from a saddle-node bifurcation, where small changes in communication or stimulus can switch the global regime.

The calcium oscillation magnitude thus encodes (multiplexes) both ATP stimulus strength and local network connectivity. Cells in this regime use communication to simultaneously propagate external signals and encode neighborhood status, providing a flexible response system well-suited for adapting to varying environments or network compositions (Potter et al., 2015).

5. Broader Impact and Generalizations

The principles uncovered generalize beyond fibroblast monolayers.

• Similar dynamics underlie collective decision-making in animal groups, where local social cues (analogous to cellular communication) optimize foraging and navigation (see (Cohen et al., 2019)).
• In artificial systems, modular architectures that combine local signal exchange and stochastic processing can prompt distributed consensus or synchronization.
• In neural or sensory prosthetic contexts, incorporating communication-inspired feedback (e.g., spatial summation across contact points (Kodali et al., 3 Apr 2024)) can enhance perceptual discrimination and response reliability.

The critical takeaway is that sensory prompting is most robust when network architectures allow for both propagation of stimulus-driven cues and integration of local connectivity information. Disruption of the communication layer—whether by biological defects or engineered decoupling—undermines the system’s sensitivity, synchrony, and adaptability.

6. Mathematical Formalization and Modeling

A critical part of understanding sensory prompting is the quantitative modeling of the underlying dynamics. The core model in the fibroblast system uses coupled nonlinear oscillators with stochasticity and diffusive coupling:

$$ε \frac{dc}{dτ} = α_1(1 - x) + α_2(1 - x) \frac{x(1 - y)}{x + β_1[1 + β_0(I)]} - \frac{x^2}{x^2 + α_3^2} + \text{diffusive terms}$$

where:

• $x$: dimensionless cytosolic Ca²⁺ concentration,
• $y$: fraction of inactivated receptors,
• $α_j, β_j$ : model parameters tuned to fit experimental data,
• $\text{diffusive terms}$: coupling with neighbors' $c$.

Cell-to-cell communication is implemented as discrete “hopping” reactions:

$$C_{(i,j)} \overset{h}{\leftrightarrow} C_{(i+1, j)}, \qquad C_{(i,j)} \overset{h}{\leftrightarrow} C_{(i, j+1)}$$

with the hopping rate $h$ constrained by experimental characterization of gap junction conductance.

The analysis yields not only time series predictions, but also distributions and higher-order statistics of ISIs and spatial correlations, connecting single-cell stochasticity to collective ensemble statistics.

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In summary, sensory prompting arises when networked units—cells, agents, or artificial modules—are driven to respond or synchronize not only by stimulus inputs, but critically by the structure and strength of inter-unit communication. Network topology, density, and heterogeneity become key parameters alongside stimulus strength in determining the character and robustness of the collective sensory response. These findings, established via combined experimental and stochastic modeling work in multicellular fibroblast networks, generalize to a broad swath of biological and engineered systems where emergent, multiplexed sensory encoding is required.