The computation biomachine

Human computers use logic gates and neural networks. Biochemical reactions can be forced to implement both, and they are bad at it. So what is the natural computational task of a cell?

CCBS · EST 5053 · Fall 2026 · lecture 12 · core page · 2026-10-20 (Tue) 10:40–12:15 · students present, lecturer-backed

The question sounds settled and is not. You can build a logic gate out of genes, and three genes can be made into a linear threshold unit, which is a perceptron. Then the arithmetic arrives: count the gates a cell has, the energy per operation, the noise, and the comparison with silicon stops flattering anybody. The lecture's real question is the one that survives: if a cell is not computing functions of inputs, what is it computing? The answer this course argues for is decisions among states, which is why multistability came first.

1Logic gates in cells

Encode 0/1 as low/high concentration; implement NAND by catalysis; NAND is universal, so a cell could, in principle, compute anything.

Take two inputs, encode them as concentration levels, and write the truth table as reactions. A NAND gate — the universal gate — is four catalysis reactions with rate constants chosen so the output flips exactly when both inputs are high:² (00→1, 01→1, 10→1, 11→0; the notes write the four reactions explicitly, X₀+Y₀+Z₀ → X₀+Y₀+Z₁ etc.). Since NAND is universal, Turing universality follows in principle: a cell could compute anything, given enough gates. That clause is where the argument turns.

2Not enough complexity

~10³ enzyme types ≈ ~3·10³ gates, against a 1972 pocket calculator's 3·10³ transistors and today's 10⁹ — and yet cells are the smarter computer.

The count, from the lecture:² E. coli has ≈10³ enzyme types — call it ≈3·10³ "logic gates." A 1972 pocket calculator had 3·10³ transistors. The Apollo guidance computer: ~5·10³ gates. A modern microcontroller: 10⁸; a laptop chip: 10⁹. The verdict written in the notes: NOT ENOUGH COMPLEXITY!! — and yet the cell runs a self-reproducing, environment-adapting chemical factory. Therefore the model is wrong: cells must compute in a format whose cost is not per-gate.

3Perceptrons, and the numbers on the other side

The unit: y = 1 iff Σwᵢxᵢ > θ. The scaling: LeNet 10⁵ weights, GPT-4 10¹² — a human cell has ~10⁴-ish. The gap is the message.

A linear threshold unit is y = 1{Σᵢ wᵢxᵢ > θ}; a network of them, deep, dominates modern AI — and its power is the depth: representational complexity grows exponentially with layers. Meanwhile, count the cell's weights: the lecture's table runs E. coli (300 TF, 1–2 per gene, ~10² weights), yeast (200 TF, 5–12 per gene, ~10³), human (1800 TF, 10–12 per gene, ~10⁴) — versus LeNet (10⁵), AlexNet (10⁷–10⁸), GPT-3 (10¹¹), GPT-4 (10¹²). A human cell sits at about a tenth of LeNet. So either cells don't compute much, or they compute in a cheaper format.

4The titration GRN is a threshold unit

Binding equilibrium + competition ⇒ R_i = max(0, R_tot − R'_tot) ⇒ Σ wⱼxⱼ < θᵢ. A threshold unit out of just three genes.

The worked derivation, in four lines of algebra:²

with per-gene expression R_i,tot = gᵢ/(1 + Σⱼ Iⱼ/K_M^ji) (using k_txk_tl/(k_pdk_pd) ≈ 1). Under tight, competitive binding the sum degrades into titration:

A linear threshold unit out of just three genes. The point is not that cells are neural networks; it is that the biochemical substrate's computational primitive (binding + competition, executed silently and in parallel) is the efficient one — and that the cost of a "weight" is one binding constant, not one enzyme.

†References & note sources

Where this page's claims and numbers live.