Synthetic neuromorphic computing in living cells

The study addresses the challenge of scaling genetic circuits in living cells to implement sophisticated sensing, processing, and actuation. Traditional digital biological circuits compute with binary levels and have enabled logic gates, memory, counters, and complex logic, while analog circuits compute over continuous values. However, both paradigms face limitations in cellular contexts due to resource constraints, stochastic fluctuations, crosstalk, and difficulties handling graded biological signals or cumulative noise. Biological systems naturally exhibit nonlinear, often logarithmic or power-law input-output relations, with outcomes driven by fold-change. Motivated by theoretical analyses showing neural-like computation in gene regulatory networks, the authors propose neuromorphic computing principles for single-cell gene circuits. They introduce the perceptgene, a log-domain analog of a perceptron, to better match biochemical nonlinearity and fold-change sensing, enabling weighted multi-input computation and activation functions suitable for classification and graded responses.

The paper situates its contribution within synthetic biology’s prior digital and analog circuit implementations, citing logic gates, memory, state machines, toggle switches, digitizers, and complex logic, as well as analog computations and control systems including oscillators and integral feedback. It highlights neuromorphic computing successes in electronics, optics, software, and DNA computing, noting efficiency in complex tasks and resource-limited contexts. The authors review biological evidence for fold-change detection, logarithmic/power-law responses, and theoretical work on neural-like behavior in gene networks. They compare neuromorphic approaches to digital and analog paradigms, emphasizing potential for fewer components, flexible decision-making via activation functions (sigmoid, rectifiers), and compatibility with iterative optimization (e.g., gradient descent/backpropagation).

• Perceptgene concept: The perceptron’s linear-domain operations (weighted sum) are recast into the logarithmic domain as power-law and multiplication. Inputs xi are raised to weights ni (effective Hill coefficients) and multiplied, forming an aggregate y that feeds a promoter-based activation function. The activation uses Michaelis-Menten-like kinetics with basal activity (z = β + y/(Km + y)), operating in log domain. Biases are set by the ratio of maximal transcription factor level to promoter binding affinity. Weights are primarily determined by Hill coefficients and circuit topology (e.g., feedback loops). Basal level β sets both output fold-change and effective threshold.
• Genetic implementation of power-law and multiplication: Two small-molecule inputs, IPTG and aTc, regulate LacI and TetR, respectively, via auto-negative feedback loops (PlacO, PtetO) to broaden dynamic range and encode power-law responses. A combinatorial promoter PlacO/tetO implements multiplicative integration of weighted inputs. Variants altering operator number (e.g., PlacO1 with one LacI site) tune cooperativity and effective weights.
• Full perceptgene with activation function: The aggregate signal controls AraC expression, which activates PBAD with Arabinose. By tuning Arabinose, PBAD/AraC behaves as different activation functions in log space: negative rectifier (low Ara), positive rectifier (high Ara), or approximately linear (very high Ara and specific AraC levels). This enables computing smooth minimum, maximum, and average operations of log-transformed inputs.
• Modeling and parameter extraction: Minimal and detailed biochemical models relate exponents to Hill coefficients and binding site numbers. Transfer functions are fit to power-law forms and perceptgene models to extract weights, input ranges (IR), maximum fold change (MFC), and Nonlinearity degree (computed as log(MFC/IR)^(1/m)). Stability over time is assessed (~10 h).
• Variants and functions:
  • Minimum: Low Arabinose yields a shifted, biased log negative rectifier at PBAD, enabling min between a threshold-related term and a weighted log input, validated by plotting log-normalized inputs/outputs.
  • Maximum: High Arabinose yields a log positive rectifier, enabling max between weighted log inputs with an offset related to one signal.
  • Average: Linear activation with total input weights ~0.5 each yields a log-domain average of two inputs.
• Multi-layer perceptgene network: A two-layer cascade computes a three-input soft majority. First-layer (AHL, IPTG) outputs T7 RNAP; second-layer integrates T7 RNAP with aTc via SupD-mediated readthrough to drive T7 promoter and GFP. Design constraints are derived using piecewise-linear approximations and transformed to log domain, guiding choices of weights, biases, and dynamic ranges (e.g., tuning AraC bias via ssrA tag, adjusting aTc weight via dual SupD sites).
• Optimization via backpropagation-inspired procedure: For the majority circuit, outputs for all eight input states are measured for both layers; normalized outputs are used to compute partial derivatives of a log-mean-squared error cost with respect to selectable weights (PBAD/AraC via Arabinose levels; Plux/AHL via operator mutations). Iterative weight updates select the next available discrete weight values.
• ADC design: Two-bit analog-to-digital conversion of AHL using perceptgenes. First design uses transcriptional interference (convergent Plux/tetO vs PBAD) to subtract MSB from LSB; revised design adds TetR control to avoid repression at high input and later splits LSB into LSB_low and LSB_high perceptgenes to improve fidelity. A ternary switch is realized by boosting LSB activation.
• Programmable logic via sequestration: ExsD sequesters ExsA to modulate internal weight and bias, enabling switching between OR and AND behaviors in a two-input perceptgene by inducing AHL to control ExsD; additional tuning via plasmid copy numbers adjusts input weights.
• Noise/SNR analysis: Single-cell measurements quantify SNR across circuit variants; effects of auto-positive vs auto-negative feedback and activation stage on SNR distributions reported.

• Introduced the perceptgene, a log-domain perceptron implemented in E. coli, with weights mapped to effective Hill coefficients and bias mapped to transcription factor capacity vs DNA affinity.
• Power-law and multiplication stage: Two-input IPTG/aTc circuit exhibits ~two orders of magnitude dynamic range per input. Fitted exponents include IPTG ~0.3375 and aTc ~0.26 (R^2 ~0.97). Modifying operator sites (e.g., PlacO to PlacO1) altered cooperativity and increased input weight; 3D transfer remains linear in log scale with Nonlinearity degree 1.33. Stability maintained for ~10 h.
• Full perceptgene with PBAD/AraC: Adding sigmoid-like activation increased Nonlinearity >3-fold (from 1.33 to 3.8; Table 1) enabling soft classification; experimental transfer functions correlate with detailed models (R^2 > 0.9).
• Smooth functions encoded:
  • Minimum (IPTG, aTc via PBAD/AraC at low Arabinose): Achieved smooth min in log space with standard error ~10% after appropriate normalization and offset (Fig. 1j).
  • Maximum (AHL, aTc via PBAD/AraC at high Arabinose): Achieved smooth max in log space with standard error ~23% (Fig. 2f). Nonlinearity degree ~2 (Table 1).
  • Average (AHL, IPTG with near-linear activation): Achieved log-average with offset −1/4 and standard error ~9% (Fig. 2i); Nonlinearity ~1.08 (near linear; Table 1). Output stable ~10 h.
• Nonlinearity degrees (Table 1 examples):
  • Power-law only: 1.03–1.33 depending on topology.
  • With sigmoid activation: 3.8.
  • With positive rectifier: 2.0.
  • With linear activation: ~1.08.
• SNR: Auto-positive feedback reduced SNR at the power-law stage compared to auto-negative; adding activation (AraC) brought SNR distributions of different circuits to similar levels.
• Soft majority function (3 inputs): Two-layer perceptgene network computed a soft majority. Initial design had 2/8 incorrect cases at high Arabinose (0.25 mM), corrected by tuning Arabinose to intermediate levels (0.031–0.0625 mM) to adjust PBAD/AraC weight, minimizing a log-MSE cost. Experimental cost function trends matched simulations.
• Backpropagation-inspired optimization: Using a discrete set of Arabinose levels and Plux operator variants (weights 0.1, 0.2, 0.27, 0.45), the algorithm reached correct majority outputs after 3 iterations using 48 samples, consistent with a precomputed cost landscape over 576 condition combinations.
• ADCs and ternary switch:
  • Two-bit ADC converting AHL to MSB/LSB with transcriptional interference-based subtraction; revised designs addressed repression at high input and improved (1,0) state via dual LSB perceptgenes. Achieved four distinct digital states; outputs stable ~10 h.
  • Reconfiguration to a ternary switch by enhancing LSB activation (high Arabinose) produced distinct low/medium/high outputs.
• Programmable logic via ExsA/ExsD sequestration: AHL-induced ExsD modulated internal weight and bias of a perceptgene to switch behavior from OR (AHL=0) to AND (AHL=0.34 µM). Strengthening auto-negative feedback loops (medium copy plasmids) increased IPTG and aTc input weights by >25%, sharpening OR behavior.
• Efficiency: A three-input soft majority required ~15 parts vs ~22 in state-of-the-art digital implementations. The neuromorphic two-bit ADC required only two transcription factors compared to multi-stage digital designs.
• Theoretical comparisons indicated log-domain computing is more suitable than linear-domain perceptrons for classifying within biological dynamic ranges and more robust to low-signal noise.

Findings demonstrate that neuromorphic design principles—specifically log-domain, fold-change-based computation—align well with biological signaling properties, enabling robust weighted integration and activation-driven classification within living cells. By mapping perceptron weights to biological Hill coefficients and biases to biophysical capacity/affinity ratios, circuits can be systematically tuned through promoter/operator engineering, feedback topology, and inducer levels. Adding activation functions markedly increases nonlinearity and supports soft/hard classification while maintaining manageable resource use and stability. The approach scales to multi-layer networks, as shown by the soft majority function, and supports iterative optimization via backpropagation-inspired weight updates based on measured outputs, bridging wet-lab experimentation and AI algorithms. The neuromorphic framework enables versatile functions (min, max, average), multi-bit ADCs, and programmable logic, offering potential advantages over purely digital or analog designs in component count, power (expression) levels, and reconfigurability. Applications include biosensing, therapeutic logic with graded outputs (e.g., safer immunotherapy via minimum operations), and robust control through averaging. The analysis also clarifies trade-offs: auto-positive feedback broadens dynamic range at the cost of SNR; activation stages can unify SNR characteristics across designs. Comparative theory suggests log-domain circuits better classify within biological constraints than linear-domain perceptrons, supporting the choice of log-based architectures.

This work introduces perceptgenes, a practical log-domain perceptron abstraction implemented in E. coli, and demonstrates a suite of neuromorphic gene circuits that compute smooth minimum, maximum, average, a 3-input soft majority via a two-layer network, two-bit ADCs, and a ternary switch. The circuits are tunable in weights and biases through promoter/operator design, feedback topologies, and inducer levels, enabling reconfiguration (e.g., AND↔OR) and optimization using backpropagation-inspired algorithms. The neuromorphic paradigm reduces part count, operates at lower expression levels, and better matches biological fold-change sensing and nonlinearity compared to traditional digital/analog designs. Future research directions include: expanding implementation modalities (protein-protein, RNA devices) and host organisms; integrating neuromorphic, digital, and analog designs into hybrid systems; developing CAD tools that combine ANN principles with logic/linear equation frameworks; and advancing data-driven experimental optimization strategies offering both coarse and fine control of weights and biases.

• Input count and integration: The number of distinct inputs per perceptgene is limited by promoter structure and the ability to integrate multiple analog signals in a single regulatory element.
• Noise and SNR: Auto-positive feedback reduces SNR at the aggregation stage; while activation can coalesce SNR distributions, noise remains a consideration, especially at low expression.
• Discrete tunability: Practical weight tuning relies on discrete changes (operator variants, copy number, inducer levels), which may limit fine-grained optimization and can introduce batch-specific variability.
• Majority circuit performance: Initial majority implementation produced incorrect states before parameter tuning; achieving robust margins may require additional elements (e.g., recombinases) to sharpen outputs.
• ADC artifacts: The first ADC design suffered from repression of maximal activation due to transcriptional interference; the improved design introduced an additional transitional state between digital outputs.
• Generalizability: While demonstrated in E. coli with specific TFs and promoters, portability to other organisms and regulatory modalities may require substantial reengineering and characterization.