# Chance ORF supply — our own calculation

Run it: `deno run html/unpublished-ai/orphan-genes/orf-supply.ts`. Source beside the article. Two independent methods (closed form from base composition, and simulation over generated sequence) agree to three significant figures, which is the check that the model is implemented correctly.

## The question

Any "de novo gene birth is too fast for evolution" argument has a supply step that almost nobody checks. Before selection can act on a new reading frame, one has to exist. If long stop-free stretches are rare in non-coding DNA, then de novo birth is supply-limited and a rate argument can be built. If they are common, no rate argument works and the debate has to move to function.

## Result

Human-sized genome, 3.1 Gb, both strands, maximal stop-free runs:

| GC | P(stop codon) | mean run | ≥50 codons | ≥100 codons | ≥150 codons | ≥200 codons |
|---|---|---|---|---|---|---|
| 41% (genome average) | 0.06135 | 16.3 codons | 1.60e7 | 6.77e5 | 2.85e4 | 1.20e3 |
| 55% (Clamp's orphan set) | 0.03923 | 25.5 codons | 3.29e7 | 4.44e6 | 6.01e5 | 8.12e4 |

**About 677,000 chance ORFs of at least 100 codons at genome-average composition.** Reading frames of protein-gene length are not scarce. They are everywhere.

## Two conclusions this forces

**1. The "too fast" argument cannot be built on scarcity of reading frames.** The raw material is abundant by six orders of magnitude over what any published de novo birth rate requires. Whatever is hard about making a new gene, *finding an open reading frame is not the hard part.* An argument that de novo genes appear too quickly has to locate its improbability somewhere else — in function, not in supply.

**2. Clamp et al.'s GC argument cuts both ways, and this appears to be unremarked.** Clamp 2007 reports the 1,177 human orphans have GC 55% against a 39-41% genome average, and reads the resemblance to real coding genes (53%) as evidence the orphans are genuine. But all three stop codons are AT-rich — TAA, TAG, TGA each carry at least two A/T — so raising GC *lowers* stop frequency and *raises* chance-ORF abundance. At 55% GC, chance ORFs of ≥100 codons are **6.6× more abundant** than at genome average (4.44e6 vs 6.77e5), and at ≥200 codons **68× more** abundant.

So elevated GC in an orphan set is exactly what one expects if those orphans are chance ORFs concentrated in GC-rich isochores. The observation does not discriminate between "real genes" and "chance ORFs" — it is predicted by both. Clamp's other evidence (reading-frame conservation) does discriminate; the GC number does not, and should not be cited as though it does.

## Caveats to state in the article

- **Real non-coding DNA is not random sequence.** It carries repeats, isochore structure, transposable-element remnants and residual constraint. This is an order-of-magnitude model, not a genome annotation. It is sufficient for the claim being made — that supply is not limiting — because the margin is six orders of magnitude, not a factor of two.
- **An ORF is not yet a gene.** It additionally needs a start codon in reasonable context, transcription, and translation. Start codons are common and transcription is pervasive, so these reduce the number without changing the conclusion. They should be stated anyway.
- The 3.1 Gb and both-strands assumptions are stated in the script and easy to change.