HOW MANY MUTATIONS TO INVENT A NEW FUNCTION?

Cells evolve new functions by mutation, but the space evolution has to search is staggering. A typical bacterial gene of 1,000 DNA letters can be written in about 10⁶⁰⁰ different ways, and each version is a single mutation away from 3,000 others. Yet experiments often find new functions within a handful of mutations: nine changed what one enzyme produces, five made another 100,000 times more resistant to an antibiotic. Does a gigantic space of possibilities make evolution slower, because the right change is hard to find — or faster, because more paths lead somewhere?

Circuits that evolve

Nida Farheen and Jané Kondev of Brandeis University, with Zachary Boroda and Ethan Levien, tackled the question with a model in which everything can be counted. Their “organisms” are small circuits: two inputs, a number N of NAND logic gates — each outputs 0 only when both its inputs are 1, and 1 otherwise — and one output. The wiring is the genotype. The logical function the circuit computes on its two inputs is the phenotype — there are only 16 possible ones.

Fitness is simple: the fraction of the four possible input pairs for which the circuit gives the target answer, so 0, 0.25, 0.5, 0.75 or 1. A mutation rewires one connection at random, keeping the number of gates fixed; rewirings that would create a loop are not allowed. Whether a mutant takes over a population of 10,000 follows a standard formula of population genetics, which favours improvements and lets neutral changes spread only rarely.

Growing N enlarges the space of possible circuits roughly like N to the power N, and gives each circuit on the order of N² neighbours one mutation away. If the 16 functions were spread evenly, the authors note, about 16 mutations would always suffice, whatever the size.

About ten mutations per gate

They started from a circuit computing NAND — every gate wired to both inputs, the output connected to gate 1 — and let it evolve towards AND, its exact opposite. For sizes from 5 to 1,000 gates, they ran 500 simulations each.

The number of mutations needed grew almost in proportion to the size of the circuit, following roughly 9.8 × N^0.96: about ten per gate. The even-spread guess of 16 is far off. Almost all those mutations were neutral — they left fitness unchanged — and never spread. At most four improvements are ever needed, since fitness climbs in steps of a quarter; the rest of the time, evolution waits.

The wires that count

Why? The authors single out computing wires: those on a path from the inputs to the output. Rewiring anything else cannot change the output. In these circuits, only about three wires compute, whatever the size, while the total number of wires is 2N + 1. So the chance of hitting a wire that matters falls like 1/N. Once a computing wire is hit, the chance that the change helps does not depend on size. Put together, it takes on the order of N attempts to land one useful mutation.

Seen as a map of all circuits, each one has about N² neighbours, but only about N of them differ by a change to a computing wire.

Change the start, change the rule

The explanation makes a prediction. Start instead from a circuit in which every wire computes, and the chance of hitting a wire that matters no longer shrinks with size. Then the number of mutations should stop growing. The simulations agreed: about 31 × N^0.07, practically flat. From the original NAND circuit, even with a much smaller population of 10, where neutral changes spread more often, the growth stayed close to linear.

There is a twist about time. Bigger circuits have more wires, so they collect mutations faster. If the number of mutations grows in proportion to N, the time to evolve AND stays the same for all sizes; if it does not, larger circuits get there sooner.

What size alone does not tell

The authors conclude that the sheer number of possible mutations does not decide how hard it is to evolve something new. What matters is the share of mutations that can improve fitness — those that touch the parts doing the computing, and among them, those that help. They are clear about the limits: their circuits have only five fitness levels and 16 possible functions, the result depends on the starting circuit, and how far it extends to real genomes is an open question. The answer to “how many mutations?” may lie less in how big a genome is than in how much of it is at work.