Analog Bio-Computers
Composed of Trinary Processors
Beyond the discrete −1 / 0 / +1 trits of a single PMBT chip lies a second, richer regime: when many trinary biochemical processors are wired together by microfluidic channels, the metal-ion concentrations flowing between them become continuous real-valued signals. The whole array stops behaving like a digital circuit and starts behaving like an analog computer — one that solves equations directly in the chemistry of its enzymes.
Each processor becomes an analog processing element whose transfer function is its enzyme kinetics. Summation happens by mixing, multiplication by coupled cascades, integration by accumulation, and differentiation by feed-forward sensing. Thousands of these elements form a reaction–diffusion fabric that natively integrates differential equations in physical time.
From discrete trits to continuous signals
A single PMBT processor quantises each metal channel into three logic states. But the underlying chemistry never truly leaves the continuum — concentrations, reaction rates and reporter intensities are smooth real numbers. An analog computer simply refuses to quantise: it keeps the full real-valued signal and computes with it directly.
| Property | Digital PMBT (trinary) | Analog array (continuous) |
|---|---|---|
| State space | Discrete { −1, 0, +1 } | Continuous concentration [M] ∈ ℝ⁺ |
| Information carrier | Operon switched on / partial / off | Real-valued metal-ion flux & reporter intensity |
| Elementary unit | Trit (1.58 bits) | Analog level (precision-limited by noise) |
| Composition law | Boolean / trinary logic gates | Superposition, Kirchhoff-like mass balance |
| Time model | Clocked transitions | Continuous real-time dynamics |
| Natural problem | Decision, classification, logic | Differential equations, optimisation, filtering |
Detoxification kinetics are inherently graded — the rate of conversion scales smoothly with metal concentration. Quantising throws this richness away. Analog mode exploits it.
Analog gains massive parallelism and native calculus, but pays in precision: each value is limited by molecular noise and cross-talk to roughly 4–6 effective bits per element.
PMBT arrays can run digital trinary logic for control and decisions, while dedicating sub-arrays to analog computation — a mixed-signal bio-computer.
The Analog Processing Element
Strip a PMBT processor down to a single metal channel and you have an Analog Processing Element (APE): a biochemical transfer function that maps an input concentration to an output signal through enzyme kinetics. Every analog computer on this page is built by wiring APEs together.
Input = metal-ion concentration [S]. Output = product / reporter flux v. The saturating curve gives a built-in soft limiter; the Hill exponent n sets analog gain and turns an APE into a tunable amplifier or comparator.
Six analog operations, realised biochemically
A classical analog computer is built from a small set of operators — adders, multipliers, integrators, differentiators. Metabolic chemistry offers a direct biochemical analogue for each, so a network of APEs can assemble these primitives into arbitrary computations.
Several APEs releasing the same product into one micro-chamber add their fluxes by simple mass balance — the analog sum of their inputs.
When one channel’s product is the substrate of another, output scales with the product of both inputs — an analog multiplier built from sequential cascades.
A sealed chamber that accumulates reaction product holds the time-integral of its input flux — the core element for solving differential equations.
An activator racing a delayed repressor produces a transient proportional to the rate of change of the input — a biochemical differentiator.
Steep cooperative response curves approximate logarithmic and exponential maps, enabling analog companding and wide dynamic range.
A zero-order ultrasensitive motif acts as an analog comparator, snapping output high once an input crosses a tunable set-point.
The biochemical operational amplifier
The op-amp is the workhorse of electronic analog computers. Its biochemical twin is an enzymatic cascade with high cooperative gain wrapped in product-inhibition feedback. Closed around different feedback chemistries, this single motif becomes an adder, an integrator, a comparator or a buffer — exactly as in silicon.
Configurable by feedback: capacitive feedback (an accumulation chamber) → integrator; resistive feedback (a leak channel) → weighted adder; no feedback → comparator.
The reaction–diffusion processor fabric
Tile APEs onto a 2D (or stacked 3D) grid and connect neighbours with microfluidic channels. Substrate diffusing between cells couples them spatially; the array as a whole becomes an analog computer whose state evolves according to a reaction–diffusion equation — computing a field, not a number.
8 × 8 tile of trinary processors — each cell an analog element, edges = diffusive coupling
Every cell computes simultaneously — the array updates as one continuous physical system, no clock required.
Channel widths set diffusion weights, turning the mesh into a programmable analog interconnect.
Pattern formation, wave propagation and gradient following emerge directly from the chemistry.
Tiles compose into wafers; multiple metals give independent, superimposed computing layers.
Problems the analog array solves natively
Because the hardware obeys the same equations as the problems, the analog bio-computer does not simulate these systems — it physically embodies them and relaxes to the answer.
Chain integrators and adders in feedback to model exponential decay, oscillators and chemical-kinetic systems in real, physical time.
The fabric natively integrates ∂u/∂t = D∇²u + f(u) — the array IS the discretised PDE, solving it as it physically evolves.
Chemotactic gradient following lets the array roll downhill on a concentration landscape, settling into minima — analog optimisation.
Weighted summation + saturating nonlinearity is exactly a neuron. Meshes of APEs perform matrix–vector products and activations as a physical neural network.
Integrator–feedback loops form low/high-pass filters that smooth or sharpen incoming chemical signals continuously.
Crossbar arrays of weighted APEs evaluate matrix–vector multiplication in a single diffusion step — the analog accelerator pattern.
Analog computers built from PMBT processors
Wiring many analog processing elements together yields whole machines, each a biochemical re-imagining of a classic analog computer. These are reference architectures — blueprints for composing tiles into purpose-built continuous solvers.
A direct descendant of Bush’s mechanical differential analyzer, rebuilt in wetware. Cascaded bio-integrators wired in feedback solve systems of ODEs in real, physical time.
Linear & non-linear ODE systems, oscillators, chemical kinetics
A 2-D sheet of coupled APE tiles that physically integrates ∂u/∂t = D∇²u + f(u). The substrate IS the discretised PDE — the answer emerges as the field relaxes.
Parabolic PDEs, pattern formation, shortest-path & maze solving
A grid of weighted APEs where each junction stores a conductance. One diffusion step performs a full matrix–vector product — the in-memory analog accelerator pattern.
Matrix–vector products, linear systems, transform kernels
Layers of summing op-amp neurons with saturating biochemical activation. Weighted metabolite fluxes feed sigmoidal gates — a physical multilayer perceptron that infers in one pass.
Classification, analog inference, associative recall
A chemotactic tile that physically rolls downhill on a concentration landscape, settling into the nearest minimum — analog optimisation with zero iterative software loop.
Continuous optimisation, energy minimisation, constraint relaxation
Proportional, integral and derivative bio-blocks combined into a closed-loop regulator that holds a chemical set-point against disturbances — control theory rendered in metabolism.
Homeostatic regulation, set-point tracking, disturbance rejection
Indicative performance envelope
Order-of-magnitude figures for a single-metal analog tile. They trade digital precision for extreme parallelism and near-thermodynamic-limit energy efficiency — the characteristic analog bargain.
concentration span per channel (nM – mM)
per analog element, noise-limited
set by enzyme turnover & diffusion
micro-chambers per chip
~10⁻¹⁹ J, near thermodynamic limit
all elements evolve concurrently
* Theoretical, exploratory estimates — not measured device specifications.
Where an analog bio-computer wins
Analog wins wherever the problem is itself continuous, parallel and physical — fields, flows, gradients and learning — and where energy budget matters more than bit-exact answers.
A sensor sheet that solves the pollutant diffusion equation in situ, mapping contamination spread in real time.
Closed-loop analog controllers modulate detox enzyme expression proportionally to live metal levels.
Trainable APE meshes perform low-power analog inference on chemical inputs — a wet neural processor.
Programmable Turing-pattern fabrics for biomaterials, tissue scaffolding and self-organising structures.
Physical gradient descent solves routing, allocation and parameter-fitting problems in chemistry.
Digital trinary logic supervises analog sub-arrays — decisions in trits, math in concentrations.