2026-08-01
The genome fits functional ensembles like cell fates but falls orders of magnitude short of exact molecular states; DNA is a generator blueprint, not a trajectory program.
DNA was pinned as the molecule of heredity in the 1950s, and the genetic code, the map from nucleotide triplets to amino acids, was cracked soon after. Given a coding sequence, the polypeptide is unambiguous. What stayed unsolved is how the same molecule specifies the rest of the organism. A bacterium is not a bag of proteins in the right ratios; a fertilized egg builds hundreds of cell types in a fixed body plan. The sequence-to-amino-acid map is solved. The genome-to-organism map is not.
This preprint (Kiiskinen and Rivas at Stanford, Kivinen at Aalto; bioRxiv, July 2026) gives the old question a hard answer from information theory: an organism simply does not carry enough organism-specific information, in its genome plus its environmental signals, to pin down its own microscopic state. The genome is a coarse generator blueprint, not a molecule-by-molecule trajectory program.
The authors model the organism as an information-processing system: a static genome g, a stream of environmental inputs U, runtime thermal noise W, and a universal compiler, the shared physical laws of electromagnetism, statistical mechanics, and chemistry, operating on a physical substrate. Two axioms hold the frame: finite state capacity, meaning any physical state carries at most log2 of the state-space size in bits; and Markovian causal locality, meaning information moves only through adjacent physical states one step at a time and cannot jump to a future step.
The core object is a coarse-graining threshold C. Partition the state space from coarse to fine, and there is a boundary: above C, the genome-plus-environment budget suffices and function can be specified; below C, programmed microstate determinism is impossible. The threshold has two complementary faces: a Shannon face governing whether you can sample the ensemble within budget, and a Hartley face governing whether you can zero in on a unique trajectory with zero error.
Three escape routes are closed. A compressed program with a stochastic decompressor does not save bits, because those relocated into runtime randomness still cost (Lemma 1). Seeding from the initial microstate fails for fast diffusive degrees of freedom, where initial-condition information decays exponentially on millisecond scales (a mixing lemma, 1b). And DNA cannot act as a clock-read delayed-trajectory tape, because transcription is triggered by present state variables such as promoter recognition and polymerase availability, not by a global clock (Lemma 2).
One careful caveat: the paper rules out programmed microstate determinism, whether the organism's own specification can fix the trajectory. It says nothing against physical determinism, whether the laws of physics fix the trajectory regardless. Physics remains deterministic; that determinism just is not written into the DNA.
Four biological cases fall on both sides of the threshold: functional, coarse descriptors sit two to three orders of magnitude below the genomic budget, while exact coordinate or trajectory descriptors exceed it.
| Case | Functional descriptor | Descriptor exceeding budget |
| Protein folding | Primary sequence 1300 bits / 300 residues | Atomic-resolution 3D 5x10^4 bits/protein; E. coli proteome is 3 to 24x the genome |
| E. coli | Copy-number vector 4.85x10^4 bits | 4 nm spatial descriptor 1.2 to 1.5x10^7 bits (genome 9.3x10^6) |
| C. elegans | Connectome 4.37x10^4 bits, lineage 8.64x10^3 | Full trajectory crosses the genome at 41.5 to 71.3 bits/cell/min |
| Drosophila | Bicoid morphogen 80 to 230 bits/nucleus/hour, enough for gap-gene fate | Not enough for a developmental microstate trajectory |
Computational verification reproduced the same structure in three off-the-shelf model classes. Across 46 AlphaFold-2 proteomes (555,846 proteins), structural output of 38.5 Gb is about 27x the 1.4 Gb coding input; charging the AlphaFold model parameters only once still leaves a 9 to 21x ratio, and the proteome-to-exome ratio stays nearly constant at 21 to 30x across species. In the JCVI-syn3A minimal-cell 4D whole-cell simulation, spatial addressability cost climbs from 60% of the genomic budget at cycle start to 139% at the end, crossing it near mid-cycle at about 4300 s. In four canonical stochastic gene networks (bursting expression, repressilator, toggle switch, MAPK cascade), coarse biochemical descriptions need only 8 to 16 bits, but refining toward spatial occupancy blows up the state space.
For anyone building biological models, the result frames what generative models can do. AlphaFold, ESMFold, and Evo generalize across organisms not because they memorize each species' microscopic program, but because they approximate the shared compiler, the physics of folding, diffusion, and chemistry. The paper draws a direct consequence: any attempt to recover a master program tape from inside an organism is bound to fail, because no such tape exists; predictive models can only approximate a compiler-style input-output map. Engineering interventions such as CRISPR and optogenetics face the same capacity bound: they bias pathways and specify ensemble behavior, but cannot script the downstream molecular trajectory.
For genetics, the paper separates heritability from genetic determinism. Heritability measures how much genetic differences explain variation in a chosen coarse phenotype, while the shared physical compiler may be causally indispensable yet contribute almost no between-individual variance, making it nearly invisible to heritability estimates. A genotype can predict a coarse phenotype with high heritability while the microscopic realization still carries entropy the genes never specified.
This is an unpeer-reviewed preprint. The impossibility result rests on two axioms and on the uniform KL contraction assumption inside the mixing lemma, and a critic can attack any of them. The mixing lemma closes the initial-condition loophole only for fast degrees of freedom; slow memory such as chromatin and epigenetics is folded into the current state and counted against the budget, a modeling choice rather than a proof that the budget fully covers them, which the authors concede needs follow-up. The empirical gaps are order-of-magnitude, and the exact threshold location depends on the coarse-graining and the entropy estimator; some of the spatial descriptors in the network and whole-cell analyses are conservative combinatorial constructions, not direct measurements. Finally, the title word "limits" is accurate: the paper rules out programmed microstate determinism, not physical determinism, and reading it as "information theory refutes biological determinism" overshoots.